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folding_nets_2d_perception_test

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2d_perception_color_75_3
What color is face 3 in the cube net shown in the image? <image_0> A. light purple B. light orange C. light red D. light green
C
color
[ "A. light purple", "B. light orange", "C. light red", "D. light green" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=2)", "faces": {"3": [[4.0, 1.0, -9.494107596574928e-16], [5.0, 1.0, 0.0], [5.0, 2.0, 0.0], [4.0, 2.0, -9.494107596574928e-16]], "5": [[5.0, 1.0, 0.0], [5.0, 1.0, 1.0], [5.0, 2.0, 1.0], [5.0, 2.0, 0.0]], "2": [[5.0, 1.0, 1.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [5.0, 2.0, 1.0]], "6": [[4.0, 1.0, 1.0], [4.0, 1.0, 0.0], [4.0, 2.0, 0.0], [4.0, 2.0, 1.0]], "1": [[4, 1, 0], [5, 1, 0], [5, 2, 0], [4, 2, 0]], "4": [[5.0, 0.9999999999999999, 0.0], [4.0, 0.9999999999999999, 0.0], [4.0, 1.0, 1.0], [5.0, 1.0, 1.0]]}, "face_connections": {"3": ["5"], "5": ["3", "2"], "2": ["5", "6", "4"], "6": ["2", "1"], "1": ["6"], "4": ["2"]}, "valid": false}, "base_face": "1", "folding_steps": [["6", "1", [4, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "6", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "2", [5.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "5", [5.0, 1.0, 0.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "2", [5.0, 1.0, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 2 downwards", "Fold face 5 downwards towards face 1", "Fold face 3 upwards towards face 6", "Fold face 4 downwards towards face 3"], "images_per_step": ["output_dir/folding_nets/random3_net15_base1_step1.png", "output_dir/folding_nets/random3_net15_base1_step2.png", "output_dir/folding_nets/random3_net15_base1_step3.png", "output_dir/folding_nets/random3_net15_base1_step4.png"], "id": "random3_net15_base1"}
2d_perception_color_75_5
What color is face 5 in the cube net shown in the image? <image_0> A. light red B. light blue C. light orange D. light green
C
color
[ "A. light red", "B. light blue", "C. light orange", "D. light green" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=2)", "faces": {"3": [[4.0, 1.0, -9.494107596574928e-16], [5.0, 1.0, 0.0], [5.0, 2.0, 0.0], [4.0, 2.0, -9.494107596574928e-16]], "5": [[5.0, 1.0, 0.0], [5.0, 1.0, 1.0], [5.0, 2.0, 1.0], [5.0, 2.0, 0.0]], "2": [[5.0, 1.0, 1.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [5.0, 2.0, 1.0]], "6": [[4.0, 1.0, 1.0], [4.0, 1.0, 0.0], [4.0, 2.0, 0.0], [4.0, 2.0, 1.0]], "1": [[4, 1, 0], [5, 1, 0], [5, 2, 0], [4, 2, 0]], "4": [[5.0, 0.9999999999999999, 0.0], [4.0, 0.9999999999999999, 0.0], [4.0, 1.0, 1.0], [5.0, 1.0, 1.0]]}, "face_connections": {"3": ["5"], "5": ["3", "2"], "2": ["5", "6", "4"], "6": ["2", "1"], "1": ["6"], "4": ["2"]}, "valid": false}, "base_face": "1", "folding_steps": [["6", "1", [4, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "6", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "2", [5.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "5", [5.0, 1.0, 0.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "2", [5.0, 1.0, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 2 downwards", "Fold face 5 downwards towards face 1", "Fold face 3 upwards towards face 6", "Fold face 4 downwards towards face 3"], "images_per_step": ["output_dir/folding_nets/random3_net15_base1_step1.png", "output_dir/folding_nets/random3_net15_base1_step2.png", "output_dir/folding_nets/random3_net15_base1_step3.png", "output_dir/folding_nets/random3_net15_base1_step4.png"], "id": "random3_net15_base1"}
2d_perception_connectivity_75_2_4
In the cube net shown in the image, is face 2 directly connected to face 4, yes or no? <image_0>
A
connectivity
[ "Yes", "No" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=2)", "faces": {"3": [[4.0, 1.0, -9.494107596574928e-16], [5.0, 1.0, 0.0], [5.0, 2.0, 0.0], [4.0, 2.0, -9.494107596574928e-16]], "5": [[5.0, 1.0, 0.0], [5.0, 1.0, 1.0], [5.0, 2.0, 1.0], [5.0, 2.0, 0.0]], "2": [[5.0, 1.0, 1.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [5.0, 2.0, 1.0]], "6": [[4.0, 1.0, 1.0], [4.0, 1.0, 0.0], [4.0, 2.0, 0.0], [4.0, 2.0, 1.0]], "1": [[4, 1, 0], [5, 1, 0], [5, 2, 0], [4, 2, 0]], "4": [[5.0, 0.9999999999999999, 0.0], [4.0, 0.9999999999999999, 0.0], [4.0, 1.0, 1.0], [5.0, 1.0, 1.0]]}, "face_connections": {"3": ["5"], "5": ["3", "2"], "2": ["5", "6", "4"], "6": ["2", "1"], "1": ["6"], "4": ["2"]}, "valid": false}, "base_face": "1", "folding_steps": [["6", "1", [4, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "6", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "2", [5.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "5", [5.0, 1.0, 0.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "2", [5.0, 1.0, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 2 downwards", "Fold face 5 downwards towards face 1", "Fold face 3 upwards towards face 6", "Fold face 4 downwards towards face 3"], "images_per_step": ["output_dir/folding_nets/random3_net15_base1_step1.png", "output_dir/folding_nets/random3_net15_base1_step2.png", "output_dir/folding_nets/random3_net15_base1_step3.png", "output_dir/folding_nets/random3_net15_base1_step4.png"], "id": "random3_net15_base1"}
2d_perception_connectivity_75_2_1
In the cube net shown in the image, is face 2 directly connected to face 1, yes or no? <image_0>
B
connectivity
[ "Yes", "No" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=2)", "faces": {"3": [[4.0, 1.0, -9.494107596574928e-16], [5.0, 1.0, 0.0], [5.0, 2.0, 0.0], [4.0, 2.0, -9.494107596574928e-16]], "5": [[5.0, 1.0, 0.0], [5.0, 1.0, 1.0], [5.0, 2.0, 1.0], [5.0, 2.0, 0.0]], "2": [[5.0, 1.0, 1.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [5.0, 2.0, 1.0]], "6": [[4.0, 1.0, 1.0], [4.0, 1.0, 0.0], [4.0, 2.0, 0.0], [4.0, 2.0, 1.0]], "1": [[4, 1, 0], [5, 1, 0], [5, 2, 0], [4, 2, 0]], "4": [[5.0, 0.9999999999999999, 0.0], [4.0, 0.9999999999999999, 0.0], [4.0, 1.0, 1.0], [5.0, 1.0, 1.0]]}, "face_connections": {"3": ["5"], "5": ["3", "2"], "2": ["5", "6", "4"], "6": ["2", "1"], "1": ["6"], "4": ["2"]}, "valid": false}, "base_face": "1", "folding_steps": [["6", "1", [4, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "6", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "2", [5.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "5", [5.0, 1.0, 0.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "2", [5.0, 1.0, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 2 downwards", "Fold face 5 downwards towards face 1", "Fold face 3 upwards towards face 6", "Fold face 4 downwards towards face 3"], "images_per_step": ["output_dir/folding_nets/random3_net15_base1_step1.png", "output_dir/folding_nets/random3_net15_base1_step2.png", "output_dir/folding_nets/random3_net15_base1_step3.png", "output_dir/folding_nets/random3_net15_base1_step4.png"], "id": "random3_net15_base1"}
2d_perception_color_76_2
What color is face 2 in the cube net shown in the image? <image_0> A. light orange B. light green C. light purple D. light red
C
color
[ "A. light orange", "B. light green", "C. light purple", "D. light red" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=3)", "faces": {"6": [[0, 1, 0], [1, 1, 0], [1, 2, 0], [0, 2, 0]], "2": [[1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0]], "5": [[1.0, 1.0, 1.0], [0.0, 1.0, 1.0000000000000002], [0.0, 2.0, 1.0000000000000002], [1.0, 2.0, 1.0]], "1": [[0.0, 1.0, 1.0000000000000002], [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [-2.83276944882399e-16, 2.0, 2.220446049250313e-16], [0.0, 2.0, 1.0000000000000002]], "3": [[-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.9999999999999997, 1.0, 9.957992501029596e-17], [0.9999999999999997, 2.0, 9.957992501029596e-17], [-2.83276944882399e-16, 2.0, 2.220446049250313e-16]], "4": [[1.0, 0.9999999999999999, 0.9999999999999999], [0.9999999999999997, 0.9999999999999999, 0.0], [-2.8327694488239893e-16, 1.0, 2.220446049250313e-16], [0.0, 1.0, 1.0000000000000002]]}, "face_connections": {"6": ["2"], "2": ["6", "5"], "5": ["2", "1"], "1": ["5", "3", "4"], "3": ["1"], "4": ["1"]}, "valid": false}, "base_face": "6", "folding_steps": [["2", "6", [1, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "2", [1.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "5", [0.0, 1.0, 1.0000000000000002], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "1", [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "1", [0.0, 1.0, 1.0000000000000002], [-2.83276944882399e-16, 0.0, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 5 downwards", "Fold face 1 downwards towards face 6", "Fold face 3 upwards towards face 6", "Fold face 4 downwards towards face 6"], "images_per_step": ["output_dir/folding_nets/random1_net16_base6_step1.png", "output_dir/folding_nets/random1_net16_base6_step2.png", "output_dir/folding_nets/random1_net16_base6_step3.png"], "id": "random1_net16_base6"}
2d_perception_color_76_1
What color is face 1 in the cube net shown in the image? <image_0> A. light orange B. light purple C. yellow D. light green
C
color
[ "A. light orange", "B. light purple", "C. yellow", "D. light green" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=3)", "faces": {"6": [[0, 1, 0], [1, 1, 0], [1, 2, 0], [0, 2, 0]], "2": [[1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0]], "5": [[1.0, 1.0, 1.0], [0.0, 1.0, 1.0000000000000002], [0.0, 2.0, 1.0000000000000002], [1.0, 2.0, 1.0]], "1": [[0.0, 1.0, 1.0000000000000002], [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [-2.83276944882399e-16, 2.0, 2.220446049250313e-16], [0.0, 2.0, 1.0000000000000002]], "3": [[-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.9999999999999997, 1.0, 9.957992501029596e-17], [0.9999999999999997, 2.0, 9.957992501029596e-17], [-2.83276944882399e-16, 2.0, 2.220446049250313e-16]], "4": [[1.0, 0.9999999999999999, 0.9999999999999999], [0.9999999999999997, 0.9999999999999999, 0.0], [-2.8327694488239893e-16, 1.0, 2.220446049250313e-16], [0.0, 1.0, 1.0000000000000002]]}, "face_connections": {"6": ["2"], "2": ["6", "5"], "5": ["2", "1"], "1": ["5", "3", "4"], "3": ["1"], "4": ["1"]}, "valid": false}, "base_face": "6", "folding_steps": [["2", "6", [1, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "2", [1.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "5", [0.0, 1.0, 1.0000000000000002], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "1", [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "1", [0.0, 1.0, 1.0000000000000002], [-2.83276944882399e-16, 0.0, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 5 downwards", "Fold face 1 downwards towards face 6", "Fold face 3 upwards towards face 6", "Fold face 4 downwards towards face 6"], "images_per_step": ["output_dir/folding_nets/random1_net16_base6_step1.png", "output_dir/folding_nets/random1_net16_base6_step2.png", "output_dir/folding_nets/random1_net16_base6_step3.png"], "id": "random1_net16_base6"}
2d_perception_connectivity_76_2_4
In the cube net shown in the image, is face 2 directly connected to face 4, yes or no? <image_0>
A
connectivity
[ "No", "Yes" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=3)", "faces": {"6": [[0, 1, 0], [1, 1, 0], [1, 2, 0], [0, 2, 0]], "2": [[1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0]], "5": [[1.0, 1.0, 1.0], [0.0, 1.0, 1.0000000000000002], [0.0, 2.0, 1.0000000000000002], [1.0, 2.0, 1.0]], "1": [[0.0, 1.0, 1.0000000000000002], [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [-2.83276944882399e-16, 2.0, 2.220446049250313e-16], [0.0, 2.0, 1.0000000000000002]], "3": [[-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.9999999999999997, 1.0, 9.957992501029596e-17], [0.9999999999999997, 2.0, 9.957992501029596e-17], [-2.83276944882399e-16, 2.0, 2.220446049250313e-16]], "4": [[1.0, 0.9999999999999999, 0.9999999999999999], [0.9999999999999997, 0.9999999999999999, 0.0], [-2.8327694488239893e-16, 1.0, 2.220446049250313e-16], [0.0, 1.0, 1.0000000000000002]]}, "face_connections": {"6": ["2"], "2": ["6", "5"], "5": ["2", "1"], "1": ["5", "3", "4"], "3": ["1"], "4": ["1"]}, "valid": false}, "base_face": "6", "folding_steps": [["2", "6", [1, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "2", [1.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "5", [0.0, 1.0, 1.0000000000000002], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "1", [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "1", [0.0, 1.0, 1.0000000000000002], [-2.83276944882399e-16, 0.0, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 5 downwards", "Fold face 1 downwards towards face 6", "Fold face 3 upwards towards face 6", "Fold face 4 downwards towards face 6"], "images_per_step": ["output_dir/folding_nets/random1_net16_base6_step1.png", "output_dir/folding_nets/random1_net16_base6_step2.png", "output_dir/folding_nets/random1_net16_base6_step3.png"], "id": "random1_net16_base6"}
2d_perception_connectivity_76_6_2
In the cube net shown in the image, is face 6 directly connected to face 2, yes or no? <image_0>
A
connectivity
[ "Yes", "No" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=3)", "faces": {"6": [[0, 1, 0], [1, 1, 0], [1, 2, 0], [0, 2, 0]], "2": [[1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0]], "5": [[1.0, 1.0, 1.0], [0.0, 1.0, 1.0000000000000002], [0.0, 2.0, 1.0000000000000002], [1.0, 2.0, 1.0]], "1": [[0.0, 1.0, 1.0000000000000002], [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [-2.83276944882399e-16, 2.0, 2.220446049250313e-16], [0.0, 2.0, 1.0000000000000002]], "3": [[-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.9999999999999997, 1.0, 9.957992501029596e-17], [0.9999999999999997, 2.0, 9.957992501029596e-17], [-2.83276944882399e-16, 2.0, 2.220446049250313e-16]], "4": [[1.0, 0.9999999999999999, 0.9999999999999999], [0.9999999999999997, 0.9999999999999999, 0.0], [-2.8327694488239893e-16, 1.0, 2.220446049250313e-16], [0.0, 1.0, 1.0000000000000002]]}, "face_connections": {"6": ["2"], "2": ["6", "5"], "5": ["2", "1"], "1": ["5", "3", "4"], "3": ["1"], "4": ["1"]}, "valid": false}, "base_face": "6", "folding_steps": [["2", "6", [1, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "2", [1.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "5", [0.0, 1.0, 1.0000000000000002], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "1", [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "1", [0.0, 1.0, 1.0000000000000002], [-2.83276944882399e-16, 0.0, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 5 downwards", "Fold face 1 downwards towards face 6", "Fold face 3 upwards towards face 6", "Fold face 4 downwards towards face 6"], "images_per_step": ["output_dir/folding_nets/random1_net16_base6_step1.png", "output_dir/folding_nets/random1_net16_base6_step2.png", "output_dir/folding_nets/random1_net16_base6_step3.png"], "id": "random1_net16_base6"}
2d_perception_color_77_4
What color is face 4 in the cube net shown in the image? <image_0> A. light blue B. yellow C. light red D. light green
A
color
[ "A. light blue", "B. yellow", "C. light red", "D. light green" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=3)", "faces": {"4": [[3.0, 1.0, 1.0000000000000002], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [3.0, 2.0, 1.0000000000000002]], "2": [[2.0, 1.0, 1.0], [2.0, 1.0, 0.0], [2.0, 2.0, 0.0], [2.0, 2.0, 1.0]], "5": [[2, 1, 0], [3, 1, 0], [3, 2, 0], [2, 2, 0]], "6": [[3.0, 1.0, 0.0], [3.0, 1.0, 1.0], [3.0, 2.0, 1.0], [3.0, 2.0, 0.0]], "1": [[3.0, 1.0, 1.0], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [3.0, 2.0, 1.0]], "3": [[2.0, 0.9999999999999999, 0.0], [2.0, 0.9999999999999999, 1.0], [3.0, 1.0, 1.0], [3.0, 1.0, 0.0]]}, "face_connections": {"4": ["2"], "2": ["4", "5"], "5": ["2", "6"], "6": ["5", "1", "3"], "1": ["6"], "3": ["6"]}, "valid": false}, "base_face": "5", "folding_steps": [["6", "5", [3, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "6", [3.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "6", [3.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["2", "5", [2, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "2", [2.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 1 downwards", "Fold face 3 inwards towards face 5", "Fold face 2 upwards towards face 1", "Fold face 4 downwards towards face 6"], "images_per_step": ["output_dir/folding_nets/random3_net16_base5_step1.png", "output_dir/folding_nets/random3_net16_base5_step2.png", "output_dir/folding_nets/random3_net16_base5_step3.png", "output_dir/folding_nets/random3_net16_base5_step4.png"], "id": "random3_net16_base5"}
2d_perception_color_77_1
What color is face 1 in the cube net shown in the image? <image_0> A. light purple B. yellow C. light red D. light orange
B
color
[ "A. light purple", "B. yellow", "C. light red", "D. light orange" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=3)", "faces": {"4": [[3.0, 1.0, 1.0000000000000002], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [3.0, 2.0, 1.0000000000000002]], "2": [[2.0, 1.0, 1.0], [2.0, 1.0, 0.0], [2.0, 2.0, 0.0], [2.0, 2.0, 1.0]], "5": [[2, 1, 0], [3, 1, 0], [3, 2, 0], [2, 2, 0]], "6": [[3.0, 1.0, 0.0], [3.0, 1.0, 1.0], [3.0, 2.0, 1.0], [3.0, 2.0, 0.0]], "1": [[3.0, 1.0, 1.0], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [3.0, 2.0, 1.0]], "3": [[2.0, 0.9999999999999999, 0.0], [2.0, 0.9999999999999999, 1.0], [3.0, 1.0, 1.0], [3.0, 1.0, 0.0]]}, "face_connections": {"4": ["2"], "2": ["4", "5"], "5": ["2", "6"], "6": ["5", "1", "3"], "1": ["6"], "3": ["6"]}, "valid": false}, "base_face": "5", "folding_steps": [["6", "5", [3, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "6", [3.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "6", [3.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["2", "5", [2, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "2", [2.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 1 downwards", "Fold face 3 inwards towards face 5", "Fold face 2 upwards towards face 1", "Fold face 4 downwards towards face 6"], "images_per_step": ["output_dir/folding_nets/random3_net16_base5_step1.png", "output_dir/folding_nets/random3_net16_base5_step2.png", "output_dir/folding_nets/random3_net16_base5_step3.png", "output_dir/folding_nets/random3_net16_base5_step4.png"], "id": "random3_net16_base5"}
2d_perception_connectivity_77_4_3
In the cube net shown in the image, is face 4 directly connected to face 3, yes or no? <image_0>
B
connectivity
[ "Yes", "No" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=3)", "faces": {"4": [[3.0, 1.0, 1.0000000000000002], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [3.0, 2.0, 1.0000000000000002]], "2": [[2.0, 1.0, 1.0], [2.0, 1.0, 0.0], [2.0, 2.0, 0.0], [2.0, 2.0, 1.0]], "5": [[2, 1, 0], [3, 1, 0], [3, 2, 0], [2, 2, 0]], "6": [[3.0, 1.0, 0.0], [3.0, 1.0, 1.0], [3.0, 2.0, 1.0], [3.0, 2.0, 0.0]], "1": [[3.0, 1.0, 1.0], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [3.0, 2.0, 1.0]], "3": [[2.0, 0.9999999999999999, 0.0], [2.0, 0.9999999999999999, 1.0], [3.0, 1.0, 1.0], [3.0, 1.0, 0.0]]}, "face_connections": {"4": ["2"], "2": ["4", "5"], "5": ["2", "6"], "6": ["5", "1", "3"], "1": ["6"], "3": ["6"]}, "valid": false}, "base_face": "5", "folding_steps": [["6", "5", [3, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "6", [3.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "6", [3.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["2", "5", [2, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "2", [2.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 1 downwards", "Fold face 3 inwards towards face 5", "Fold face 2 upwards towards face 1", "Fold face 4 downwards towards face 6"], "images_per_step": ["output_dir/folding_nets/random3_net16_base5_step1.png", "output_dir/folding_nets/random3_net16_base5_step2.png", "output_dir/folding_nets/random3_net16_base5_step3.png", "output_dir/folding_nets/random3_net16_base5_step4.png"], "id": "random3_net16_base5"}
2d_perception_connectivity_77_2_5
In the cube net shown in the image, is face 2 directly connected to face 5, yes or no? <image_0>
B
connectivity
[ "No", "Yes" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=3)", "faces": {"4": [[3.0, 1.0, 1.0000000000000002], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [3.0, 2.0, 1.0000000000000002]], "2": [[2.0, 1.0, 1.0], [2.0, 1.0, 0.0], [2.0, 2.0, 0.0], [2.0, 2.0, 1.0]], "5": [[2, 1, 0], [3, 1, 0], [3, 2, 0], [2, 2, 0]], "6": [[3.0, 1.0, 0.0], [3.0, 1.0, 1.0], [3.0, 2.0, 1.0], [3.0, 2.0, 0.0]], "1": [[3.0, 1.0, 1.0], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [3.0, 2.0, 1.0]], "3": [[2.0, 0.9999999999999999, 0.0], [2.0, 0.9999999999999999, 1.0], [3.0, 1.0, 1.0], [3.0, 1.0, 0.0]]}, "face_connections": {"4": ["2"], "2": ["4", "5"], "5": ["2", "6"], "6": ["5", "1", "3"], "1": ["6"], "3": ["6"]}, "valid": false}, "base_face": "5", "folding_steps": [["6", "5", [3, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "6", [3.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "6", [3.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["2", "5", [2, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "2", [2.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 1 downwards", "Fold face 3 inwards towards face 5", "Fold face 2 upwards towards face 1", "Fold face 4 downwards towards face 6"], "images_per_step": ["output_dir/folding_nets/random3_net16_base5_step1.png", "output_dir/folding_nets/random3_net16_base5_step2.png", "output_dir/folding_nets/random3_net16_base5_step3.png", "output_dir/folding_nets/random3_net16_base5_step4.png"], "id": "random3_net16_base5"}
2d_perception_color_78_3
What color is face 3 in the cube net shown in the image? <image_0> A. light purple B. light orange C. light green D. light red
D
color
[ "A. light purple", "B. light orange", "C. light green", "D. light red" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=2)", "faces": {"3": [[4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [4.0, 2.0, 0.0]], "5": [[4.0, 1.0, 1.0], [3.0, 1.0, 1.0], [3.0, 2.0, 1.0], [4.0, 2.0, 1.0]], "2": [[3.0, 1.0, 1.0], [3.0, 1.0, 0.0], [3.0, 2.0, 0.0], [3.0, 2.0, 1.0]], "6": [[3, 1, 0], [4, 1, 0], [4, 2, 0], [3, 2, 0]], "1": [[4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [4.0, 2.0, 0.0]], "4": [[4.0, 0.9999999999999999, 1.0], [4.0, 0.9999999999999999, 0.0], [3.0, 1.0, 0.0], [3.0, 1.0, 1.0]]}, "face_connections": {"3": ["5"], "5": ["3", "2"], "2": ["5", "6", "4"], "6": ["2", "1"], "1": ["6"], "4": ["2"]}, "valid": false}, "base_face": "6", "folding_steps": [["1", "6", [4, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["2", "6", [3, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "2", [3.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "5", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "2", [3.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 2 upwards", "Fold face 5 downwards towards face 1", "Fold face 3 downwards towards face 6", "Fold face 4 inwards towards face 3"], "images_per_step": ["output_dir/folding_nets/random3_net15_base6_step1.png", "output_dir/folding_nets/random3_net15_base6_step2.png", "output_dir/folding_nets/random3_net15_base6_step3.png", "output_dir/folding_nets/random3_net15_base6_step4.png"], "id": "random3_net15_base6"}
2d_perception_color_78_2
What color is face 2 in the cube net shown in the image? <image_0> A. light green B. yellow C. light blue D. light purple
D
color
[ "A. light green", "B. yellow", "C. light blue", "D. light purple" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=2)", "faces": {"3": [[4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [4.0, 2.0, 0.0]], "5": [[4.0, 1.0, 1.0], [3.0, 1.0, 1.0], [3.0, 2.0, 1.0], [4.0, 2.0, 1.0]], "2": [[3.0, 1.0, 1.0], [3.0, 1.0, 0.0], [3.0, 2.0, 0.0], [3.0, 2.0, 1.0]], "6": [[3, 1, 0], [4, 1, 0], [4, 2, 0], [3, 2, 0]], "1": [[4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [4.0, 2.0, 0.0]], "4": [[4.0, 0.9999999999999999, 1.0], [4.0, 0.9999999999999999, 0.0], [3.0, 1.0, 0.0], [3.0, 1.0, 1.0]]}, "face_connections": {"3": ["5"], "5": ["3", "2"], "2": ["5", "6", "4"], "6": ["2", "1"], "1": ["6"], "4": ["2"]}, "valid": false}, "base_face": "6", "folding_steps": [["1", "6", [4, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["2", "6", [3, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "2", [3.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "5", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "2", [3.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 2 upwards", "Fold face 5 downwards towards face 1", "Fold face 3 downwards towards face 6", "Fold face 4 inwards towards face 3"], "images_per_step": ["output_dir/folding_nets/random3_net15_base6_step1.png", "output_dir/folding_nets/random3_net15_base6_step2.png", "output_dir/folding_nets/random3_net15_base6_step3.png", "output_dir/folding_nets/random3_net15_base6_step4.png"], "id": "random3_net15_base6"}
2d_perception_connectivity_78_3_4
In the cube net shown in the image, is face 3 directly connected to face 4, yes or no? <image_0>
B
connectivity
[ "Yes", "No" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=2)", "faces": {"3": [[4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [4.0, 2.0, 0.0]], "5": [[4.0, 1.0, 1.0], [3.0, 1.0, 1.0], [3.0, 2.0, 1.0], [4.0, 2.0, 1.0]], "2": [[3.0, 1.0, 1.0], [3.0, 1.0, 0.0], [3.0, 2.0, 0.0], [3.0, 2.0, 1.0]], "6": [[3, 1, 0], [4, 1, 0], [4, 2, 0], [3, 2, 0]], "1": [[4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [4.0, 2.0, 0.0]], "4": [[4.0, 0.9999999999999999, 1.0], [4.0, 0.9999999999999999, 0.0], [3.0, 1.0, 0.0], [3.0, 1.0, 1.0]]}, "face_connections": {"3": ["5"], "5": ["3", "2"], "2": ["5", "6", "4"], "6": ["2", "1"], "1": ["6"], "4": ["2"]}, "valid": false}, "base_face": "6", "folding_steps": [["1", "6", [4, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["2", "6", [3, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "2", [3.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "5", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "2", [3.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 2 upwards", "Fold face 5 downwards towards face 1", "Fold face 3 downwards towards face 6", "Fold face 4 inwards towards face 3"], "images_per_step": ["output_dir/folding_nets/random3_net15_base6_step1.png", "output_dir/folding_nets/random3_net15_base6_step2.png", "output_dir/folding_nets/random3_net15_base6_step3.png", "output_dir/folding_nets/random3_net15_base6_step4.png"], "id": "random3_net15_base6"}
2d_perception_connectivity_78_2_1
In the cube net shown in the image, is face 2 directly connected to face 1, yes or no? <image_0>
A
connectivity
[ "No", "Yes" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=2)", "faces": {"3": [[4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [4.0, 2.0, 0.0]], "5": [[4.0, 1.0, 1.0], [3.0, 1.0, 1.0], [3.0, 2.0, 1.0], [4.0, 2.0, 1.0]], "2": [[3.0, 1.0, 1.0], [3.0, 1.0, 0.0], [3.0, 2.0, 0.0], [3.0, 2.0, 1.0]], "6": [[3, 1, 0], [4, 1, 0], [4, 2, 0], [3, 2, 0]], "1": [[4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [4.0, 2.0, 0.0]], "4": [[4.0, 0.9999999999999999, 1.0], [4.0, 0.9999999999999999, 0.0], [3.0, 1.0, 0.0], [3.0, 1.0, 1.0]]}, "face_connections": {"3": ["5"], "5": ["3", "2"], "2": ["5", "6", "4"], "6": ["2", "1"], "1": ["6"], "4": ["2"]}, "valid": false}, "base_face": "6", "folding_steps": [["1", "6", [4, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["2", "6", [3, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "2", [3.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "5", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "2", [3.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 2 upwards", "Fold face 5 downwards towards face 1", "Fold face 3 downwards towards face 6", "Fold face 4 inwards towards face 3"], "images_per_step": ["output_dir/folding_nets/random3_net15_base6_step1.png", "output_dir/folding_nets/random3_net15_base6_step2.png", "output_dir/folding_nets/random3_net15_base6_step3.png", "output_dir/folding_nets/random3_net15_base6_step4.png"], "id": "random3_net15_base6"}
2d_perception_color_79_4
What color is face 4 in the cube net shown in the image? <image_0> A. light purple B. light orange C. light blue D. light red
C
color
[ "A. light purple", "B. light orange", "C. light blue", "D. light red" ]
{"initial_net": {"name": "Invalid D", "faces": {"1": [[2.0, 0.9999999999999999, -1.0], [2.0, 0.9999999999999999, -1.1102230246251565e-16], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, -1.0]], "2": [[0.9999999999999999, 1.0, -1.0], [1.0, 1.0, 0.0], [1.0, 2.0, 0.0], [0.9999999999999999, 2.0, -1.0]], "3": [[1, 1, 0], [1, 2, 0], [2, 2, 0], [2, 1, 0]], "4": [[1.0, 2.0, 0.0], [2.0, 2.0, 0.0], [2.0, 2.0, -1.0], [1.0, 2.0, -1.0]], "5": [[2.0, 2.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, -1.0], [2.0, 2.0, -1.0]], "6": [[2.0, 1.0, 0.0], [1.0, 0.9999999999999999, 0.0], [1.0, 0.9999999999999999, -1.0], [2.0, 1.0, -1.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": false}, "base_face": "3", "folding_steps": [["4", "3", [1, 2, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["5", "4", [2.0, 2.0, 0.0], [0.0, 0.0, -1.0], 1.5707963267948966], ["6", "5", [2.0, 1.0, 0.0], [0.0, 0.0, -1.0], 1.5707963267948966], ["2", "3", [1, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "2", [0.9999999999999999, 1.0, -1.0], [1.1102230246251565e-16, 0.0, 1.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 5 inwards towards face 3", "Fold face 6 inwards towards face 3", "Fold face 2 upwards towards face 4", "Fold face 1 inwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net19_base3_step1.png", "output_dir/folding_nets/net19_base3_step2.png", "output_dir/folding_nets/net19_base3_step3.png", "output_dir/folding_nets/net19_base3_step4.png"], "id": "net19_base3"}
2d_perception_color_79_1
What color is face 1 in the cube net shown in the image? <image_0> A. yellow B. light blue C. light purple D. light orange
A
color
[ "A. yellow", "B. light blue", "C. light purple", "D. light orange" ]
{"initial_net": {"name": "Invalid D", "faces": {"1": [[2.0, 0.9999999999999999, -1.0], [2.0, 0.9999999999999999, -1.1102230246251565e-16], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, -1.0]], "2": [[0.9999999999999999, 1.0, -1.0], [1.0, 1.0, 0.0], [1.0, 2.0, 0.0], [0.9999999999999999, 2.0, -1.0]], "3": [[1, 1, 0], [1, 2, 0], [2, 2, 0], [2, 1, 0]], "4": [[1.0, 2.0, 0.0], [2.0, 2.0, 0.0], [2.0, 2.0, -1.0], [1.0, 2.0, -1.0]], "5": [[2.0, 2.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, -1.0], [2.0, 2.0, -1.0]], "6": [[2.0, 1.0, 0.0], [1.0, 0.9999999999999999, 0.0], [1.0, 0.9999999999999999, -1.0], [2.0, 1.0, -1.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": false}, "base_face": "3", "folding_steps": [["4", "3", [1, 2, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["5", "4", [2.0, 2.0, 0.0], [0.0, 0.0, -1.0], 1.5707963267948966], ["6", "5", [2.0, 1.0, 0.0], [0.0, 0.0, -1.0], 1.5707963267948966], ["2", "3", [1, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "2", [0.9999999999999999, 1.0, -1.0], [1.1102230246251565e-16, 0.0, 1.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 5 inwards towards face 3", "Fold face 6 inwards towards face 3", "Fold face 2 upwards towards face 4", "Fold face 1 inwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net19_base3_step1.png", "output_dir/folding_nets/net19_base3_step2.png", "output_dir/folding_nets/net19_base3_step3.png", "output_dir/folding_nets/net19_base3_step4.png"], "id": "net19_base3"}
2d_perception_connectivity_79_2_6
In the cube net shown in the image, is face 2 directly connected to face 6, yes or no? <image_0>
B
connectivity
[ "Yes", "No" ]
{"initial_net": {"name": "Invalid D", "faces": {"1": [[2.0, 0.9999999999999999, -1.0], [2.0, 0.9999999999999999, -1.1102230246251565e-16], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, -1.0]], "2": [[0.9999999999999999, 1.0, -1.0], [1.0, 1.0, 0.0], [1.0, 2.0, 0.0], [0.9999999999999999, 2.0, -1.0]], "3": [[1, 1, 0], [1, 2, 0], [2, 2, 0], [2, 1, 0]], "4": [[1.0, 2.0, 0.0], [2.0, 2.0, 0.0], [2.0, 2.0, -1.0], [1.0, 2.0, -1.0]], "5": [[2.0, 2.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, -1.0], [2.0, 2.0, -1.0]], "6": [[2.0, 1.0, 0.0], [1.0, 0.9999999999999999, 0.0], [1.0, 0.9999999999999999, -1.0], [2.0, 1.0, -1.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": false}, "base_face": "3", "folding_steps": [["4", "3", [1, 2, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["5", "4", [2.0, 2.0, 0.0], [0.0, 0.0, -1.0], 1.5707963267948966], ["6", "5", [2.0, 1.0, 0.0], [0.0, 0.0, -1.0], 1.5707963267948966], ["2", "3", [1, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "2", [0.9999999999999999, 1.0, -1.0], [1.1102230246251565e-16, 0.0, 1.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 5 inwards towards face 3", "Fold face 6 inwards towards face 3", "Fold face 2 upwards towards face 4", "Fold face 1 inwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net19_base3_step1.png", "output_dir/folding_nets/net19_base3_step2.png", "output_dir/folding_nets/net19_base3_step3.png", "output_dir/folding_nets/net19_base3_step4.png"], "id": "net19_base3"}
2d_perception_connectivity_79_1_6
In the cube net shown in the image, is face 1 directly connected to face 6, yes or no? <image_0>
B
connectivity
[ "Yes", "No" ]
{"initial_net": {"name": "Invalid D", "faces": {"1": [[2.0, 0.9999999999999999, -1.0], [2.0, 0.9999999999999999, -1.1102230246251565e-16], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, -1.0]], "2": [[0.9999999999999999, 1.0, -1.0], [1.0, 1.0, 0.0], [1.0, 2.0, 0.0], [0.9999999999999999, 2.0, -1.0]], "3": [[1, 1, 0], [1, 2, 0], [2, 2, 0], [2, 1, 0]], "4": [[1.0, 2.0, 0.0], [2.0, 2.0, 0.0], [2.0, 2.0, -1.0], [1.0, 2.0, -1.0]], "5": [[2.0, 2.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, -1.0], [2.0, 2.0, -1.0]], "6": [[2.0, 1.0, 0.0], [1.0, 0.9999999999999999, 0.0], [1.0, 0.9999999999999999, -1.0], [2.0, 1.0, -1.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": false}, "base_face": "3", "folding_steps": [["4", "3", [1, 2, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["5", "4", [2.0, 2.0, 0.0], [0.0, 0.0, -1.0], 1.5707963267948966], ["6", "5", [2.0, 1.0, 0.0], [0.0, 0.0, -1.0], 1.5707963267948966], ["2", "3", [1, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "2", [0.9999999999999999, 1.0, -1.0], [1.1102230246251565e-16, 0.0, 1.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 5 inwards towards face 3", "Fold face 6 inwards towards face 3", "Fold face 2 upwards towards face 4", "Fold face 1 inwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net19_base3_step1.png", "output_dir/folding_nets/net19_base3_step2.png", "output_dir/folding_nets/net19_base3_step3.png", "output_dir/folding_nets/net19_base3_step4.png"], "id": "net19_base3"}
2d_perception_color_80_1
What color is face 1 in the cube net shown in the image? <image_0> A. light orange B. light green C. light red D. yellow
D
color
[ "A. light orange", "B. light green", "C. light red", "D. yellow" ]
{"initial_net": {"name": "2-2 net", "faces": {"3": [[0.9999999999999999, 3.0, 1.0], [1.0, 3.0, 0.0], [2.0, 3.0, 1.1102230246251565e-16], [2.0, 3.0, 1.0]], "1": [[0.9999999999999999, 2.0, 1.0], [1.0, 2.0, 0.0], [1.0, 3.0, 0.0], [0.9999999999999999, 3.0, 1.0]], "2": [[1, 2, 0], [2, 2, 0], [2, 3, 0], [1, 3, 0]], "5": [[1.0, 2.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0], [1.0, 2.0, 0.0]], "4": [[2.0, 2.0, 1.0], [2.0, 3.0, 1.0], [2.0, 3.0, 0.0], [2.0, 2.0, 0.0]], "6": [[1.0, 2.0, 1.0], [1.0, 3.0, 1.0000000000000004], [2.0, 3.0, 1.0], [2.0, 2.0, 1.0]]}, "face_connections": {"3": ["1"], "1": ["3", "2"], "2": ["1", "5"], "5": ["2", "4"], "4": ["5", "6"], "6": ["4"]}, "valid": true}, "base_face": "2", "folding_steps": [["1", "2", [1, 2, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "2", [1, 2, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["3", "1", [1.0, 3.0, 0.0], [-1.1102230246251565e-16, 0.0, 1.0], -1.5707963267948966], ["4", "5", [2.0, 2.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["6", "4", [2.0, 2.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 5 upwards towards face 1", "Fold face 3 inwards towards face 2", "Fold face 4 inwards towards face 3", "Fold face 6 downwards towards face 3"], "images_per_step": ["output_dir/folding_nets/random3_net8_base2_step1.png", "output_dir/folding_nets/random3_net8_base2_step2.png", "output_dir/folding_nets/random3_net8_base2_step3.png", "output_dir/folding_nets/random3_net8_base2_step4.png", "output_dir/folding_nets/random3_net8_base2_step5.png", "output_dir/folding_nets/random3_net8_base2_step6.png"], "id": "random3_net8_base2"}
2d_perception_color_80_6
What color is face 6 in the cube net shown in the image? <image_0> A. yellow B. light green C. light red D. light blue
B
color
[ "A. yellow", "B. light green", "C. light red", "D. light blue" ]
{"initial_net": {"name": "2-2 net", "faces": {"3": [[0.9999999999999999, 3.0, 1.0], [1.0, 3.0, 0.0], [2.0, 3.0, 1.1102230246251565e-16], [2.0, 3.0, 1.0]], "1": [[0.9999999999999999, 2.0, 1.0], [1.0, 2.0, 0.0], [1.0, 3.0, 0.0], [0.9999999999999999, 3.0, 1.0]], "2": [[1, 2, 0], [2, 2, 0], [2, 3, 0], [1, 3, 0]], "5": [[1.0, 2.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0], [1.0, 2.0, 0.0]], "4": [[2.0, 2.0, 1.0], [2.0, 3.0, 1.0], [2.0, 3.0, 0.0], [2.0, 2.0, 0.0]], "6": [[1.0, 2.0, 1.0], [1.0, 3.0, 1.0000000000000004], [2.0, 3.0, 1.0], [2.0, 2.0, 1.0]]}, "face_connections": {"3": ["1"], "1": ["3", "2"], "2": ["1", "5"], "5": ["2", "4"], "4": ["5", "6"], "6": ["4"]}, "valid": true}, "base_face": "2", "folding_steps": [["1", "2", [1, 2, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "2", [1, 2, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["3", "1", [1.0, 3.0, 0.0], [-1.1102230246251565e-16, 0.0, 1.0], -1.5707963267948966], ["4", "5", [2.0, 2.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["6", "4", [2.0, 2.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 5 upwards towards face 1", "Fold face 3 inwards towards face 2", "Fold face 4 inwards towards face 3", "Fold face 6 downwards towards face 3"], "images_per_step": ["output_dir/folding_nets/random3_net8_base2_step1.png", "output_dir/folding_nets/random3_net8_base2_step2.png", "output_dir/folding_nets/random3_net8_base2_step3.png", "output_dir/folding_nets/random3_net8_base2_step4.png", "output_dir/folding_nets/random3_net8_base2_step5.png", "output_dir/folding_nets/random3_net8_base2_step6.png"], "id": "random3_net8_base2"}
2d_perception_connectivity_80_1_6
In the cube net shown in the image, is face 1 directly connected to face 6, yes or no? <image_0>
A
connectivity
[ "No", "Yes" ]
{"initial_net": {"name": "2-2 net", "faces": {"3": [[0.9999999999999999, 3.0, 1.0], [1.0, 3.0, 0.0], [2.0, 3.0, 1.1102230246251565e-16], [2.0, 3.0, 1.0]], "1": [[0.9999999999999999, 2.0, 1.0], [1.0, 2.0, 0.0], [1.0, 3.0, 0.0], [0.9999999999999999, 3.0, 1.0]], "2": [[1, 2, 0], [2, 2, 0], [2, 3, 0], [1, 3, 0]], "5": [[1.0, 2.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0], [1.0, 2.0, 0.0]], "4": [[2.0, 2.0, 1.0], [2.0, 3.0, 1.0], [2.0, 3.0, 0.0], [2.0, 2.0, 0.0]], "6": [[1.0, 2.0, 1.0], [1.0, 3.0, 1.0000000000000004], [2.0, 3.0, 1.0], [2.0, 2.0, 1.0]]}, "face_connections": {"3": ["1"], "1": ["3", "2"], "2": ["1", "5"], "5": ["2", "4"], "4": ["5", "6"], "6": ["4"]}, "valid": true}, "base_face": "2", "folding_steps": [["1", "2", [1, 2, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "2", [1, 2, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["3", "1", [1.0, 3.0, 0.0], [-1.1102230246251565e-16, 0.0, 1.0], -1.5707963267948966], ["4", "5", [2.0, 2.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["6", "4", [2.0, 2.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 5 upwards towards face 1", "Fold face 3 inwards towards face 2", "Fold face 4 inwards towards face 3", "Fold face 6 downwards towards face 3"], "images_per_step": ["output_dir/folding_nets/random3_net8_base2_step1.png", "output_dir/folding_nets/random3_net8_base2_step2.png", "output_dir/folding_nets/random3_net8_base2_step3.png", "output_dir/folding_nets/random3_net8_base2_step4.png", "output_dir/folding_nets/random3_net8_base2_step5.png", "output_dir/folding_nets/random3_net8_base2_step6.png"], "id": "random3_net8_base2"}
2d_perception_connectivity_80_3_5
In the cube net shown in the image, is face 3 directly connected to face 5, yes or no? <image_0>
B
connectivity
[ "Yes", "No" ]
{"initial_net": {"name": "2-2 net", "faces": {"3": [[0.9999999999999999, 3.0, 1.0], [1.0, 3.0, 0.0], [2.0, 3.0, 1.1102230246251565e-16], [2.0, 3.0, 1.0]], "1": [[0.9999999999999999, 2.0, 1.0], [1.0, 2.0, 0.0], [1.0, 3.0, 0.0], [0.9999999999999999, 3.0, 1.0]], "2": [[1, 2, 0], [2, 2, 0], [2, 3, 0], [1, 3, 0]], "5": [[1.0, 2.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0], [1.0, 2.0, 0.0]], "4": [[2.0, 2.0, 1.0], [2.0, 3.0, 1.0], [2.0, 3.0, 0.0], [2.0, 2.0, 0.0]], "6": [[1.0, 2.0, 1.0], [1.0, 3.0, 1.0000000000000004], [2.0, 3.0, 1.0], [2.0, 2.0, 1.0]]}, "face_connections": {"3": ["1"], "1": ["3", "2"], "2": ["1", "5"], "5": ["2", "4"], "4": ["5", "6"], "6": ["4"]}, "valid": true}, "base_face": "2", "folding_steps": [["1", "2", [1, 2, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "2", [1, 2, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["3", "1", [1.0, 3.0, 0.0], [-1.1102230246251565e-16, 0.0, 1.0], -1.5707963267948966], ["4", "5", [2.0, 2.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["6", "4", [2.0, 2.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 5 upwards towards face 1", "Fold face 3 inwards towards face 2", "Fold face 4 inwards towards face 3", "Fold face 6 downwards towards face 3"], "images_per_step": ["output_dir/folding_nets/random3_net8_base2_step1.png", "output_dir/folding_nets/random3_net8_base2_step2.png", "output_dir/folding_nets/random3_net8_base2_step3.png", "output_dir/folding_nets/random3_net8_base2_step4.png", "output_dir/folding_nets/random3_net8_base2_step5.png", "output_dir/folding_nets/random3_net8_base2_step6.png"], "id": "random3_net8_base2"}
2d_perception_color_81_3
What color is face 3 in the cube net shown in the image? <image_0> A. light blue B. light green C. yellow D. light red
D
color
[ "A. light blue", "B. light green", "C. yellow", "D. light red" ]
{"initial_net": {"name": "Invalid D", "faces": {"1": [[3.0000000000000004, 3.0000000000000004, 2.220446049250313e-16], [3.0000000000000004, 2.0, 0.0], [3.0, 2.0, 1.0], [3.0, 3.0, 1.0000000000000002]], "2": [[3.0, 3.0, 1.0000000000000002], [3.0, 2.0, 1.0], [2.0, 2.0, 1.0], [2.0, 3.0, 1.0000000000000002]], "3": [[3.0, 2.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0], [3.0, 2.0, 0.0]], "4": [[2.0, 2.0, 1.0], [2.0, 2.0, 0.0], [2.0, 3.0, 0.0], [2.0, 3.0, 1.0]], "5": [[2, 2, 0], [3, 2, 0], [3, 3, 0], [2, 3, 0]], "6": [[3.0, 2.0, 0.0], [3.0, 2.0, 1.0], [3.0, 3.0, 1.0], [3.0, 3.0, 0.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": false}, "base_face": "5", "folding_steps": [["6", "5", [3, 2, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "5", [2, 2, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "4", [2.0, 2.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["2", "3", [3.0, 2.0, 1.0], [-1.0, 0.0, 0.0], 1.5707963267948966], ["1", "2", [3.0, 3.0, 1.0000000000000002], [0.0, -1.0, -2.220446049250313e-16], -1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 4 upwards", "Fold face 3 inwards towards face 5", "Fold face 2 downwards towards face 4", "Fold face 1 downwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net19_base5_step1.png", "output_dir/folding_nets/net19_base5_step2.png", "output_dir/folding_nets/net19_base5_step3.png", "output_dir/folding_nets/net19_base5_step4.png"], "id": "net19_base5"}
2d_perception_color_81_5
What color is face 5 in the cube net shown in the image? <image_0> A. light orange B. light red C. light blue D. light green
A
color
[ "A. light orange", "B. light red", "C. light blue", "D. light green" ]
{"initial_net": {"name": "Invalid D", "faces": {"1": [[3.0000000000000004, 3.0000000000000004, 2.220446049250313e-16], [3.0000000000000004, 2.0, 0.0], [3.0, 2.0, 1.0], [3.0, 3.0, 1.0000000000000002]], "2": [[3.0, 3.0, 1.0000000000000002], [3.0, 2.0, 1.0], [2.0, 2.0, 1.0], [2.0, 3.0, 1.0000000000000002]], "3": [[3.0, 2.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0], [3.0, 2.0, 0.0]], "4": [[2.0, 2.0, 1.0], [2.0, 2.0, 0.0], [2.0, 3.0, 0.0], [2.0, 3.0, 1.0]], "5": [[2, 2, 0], [3, 2, 0], [3, 3, 0], [2, 3, 0]], "6": [[3.0, 2.0, 0.0], [3.0, 2.0, 1.0], [3.0, 3.0, 1.0], [3.0, 3.0, 0.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": false}, "base_face": "5", "folding_steps": [["6", "5", [3, 2, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "5", [2, 2, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "4", [2.0, 2.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["2", "3", [3.0, 2.0, 1.0], [-1.0, 0.0, 0.0], 1.5707963267948966], ["1", "2", [3.0, 3.0, 1.0000000000000002], [0.0, -1.0, -2.220446049250313e-16], -1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 4 upwards", "Fold face 3 inwards towards face 5", "Fold face 2 downwards towards face 4", "Fold face 1 downwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net19_base5_step1.png", "output_dir/folding_nets/net19_base5_step2.png", "output_dir/folding_nets/net19_base5_step3.png", "output_dir/folding_nets/net19_base5_step4.png"], "id": "net19_base5"}
2d_perception_connectivity_81_4_6
In the cube net shown in the image, is face 4 directly connected to face 6, yes or no? <image_0>
A
connectivity
[ "No", "Yes" ]
{"initial_net": {"name": "Invalid D", "faces": {"1": [[3.0000000000000004, 3.0000000000000004, 2.220446049250313e-16], [3.0000000000000004, 2.0, 0.0], [3.0, 2.0, 1.0], [3.0, 3.0, 1.0000000000000002]], "2": [[3.0, 3.0, 1.0000000000000002], [3.0, 2.0, 1.0], [2.0, 2.0, 1.0], [2.0, 3.0, 1.0000000000000002]], "3": [[3.0, 2.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0], [3.0, 2.0, 0.0]], "4": [[2.0, 2.0, 1.0], [2.0, 2.0, 0.0], [2.0, 3.0, 0.0], [2.0, 3.0, 1.0]], "5": [[2, 2, 0], [3, 2, 0], [3, 3, 0], [2, 3, 0]], "6": [[3.0, 2.0, 0.0], [3.0, 2.0, 1.0], [3.0, 3.0, 1.0], [3.0, 3.0, 0.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": false}, "base_face": "5", "folding_steps": [["6", "5", [3, 2, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "5", [2, 2, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "4", [2.0, 2.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["2", "3", [3.0, 2.0, 1.0], [-1.0, 0.0, 0.0], 1.5707963267948966], ["1", "2", [3.0, 3.0, 1.0000000000000002], [0.0, -1.0, -2.220446049250313e-16], -1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 4 upwards", "Fold face 3 inwards towards face 5", "Fold face 2 downwards towards face 4", "Fold face 1 downwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net19_base5_step1.png", "output_dir/folding_nets/net19_base5_step2.png", "output_dir/folding_nets/net19_base5_step3.png", "output_dir/folding_nets/net19_base5_step4.png"], "id": "net19_base5"}
2d_perception_connectivity_81_1_5
In the cube net shown in the image, is face 1 directly connected to face 5, yes or no? <image_0>
B
connectivity
[ "Yes", "No" ]
{"initial_net": {"name": "Invalid D", "faces": {"1": [[3.0000000000000004, 3.0000000000000004, 2.220446049250313e-16], [3.0000000000000004, 2.0, 0.0], [3.0, 2.0, 1.0], [3.0, 3.0, 1.0000000000000002]], "2": [[3.0, 3.0, 1.0000000000000002], [3.0, 2.0, 1.0], [2.0, 2.0, 1.0], [2.0, 3.0, 1.0000000000000002]], "3": [[3.0, 2.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0], [3.0, 2.0, 0.0]], "4": [[2.0, 2.0, 1.0], [2.0, 2.0, 0.0], [2.0, 3.0, 0.0], [2.0, 3.0, 1.0]], "5": [[2, 2, 0], [3, 2, 0], [3, 3, 0], [2, 3, 0]], "6": [[3.0, 2.0, 0.0], [3.0, 2.0, 1.0], [3.0, 3.0, 1.0], [3.0, 3.0, 0.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": false}, "base_face": "5", "folding_steps": [["6", "5", [3, 2, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "5", [2, 2, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "4", [2.0, 2.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["2", "3", [3.0, 2.0, 1.0], [-1.0, 0.0, 0.0], 1.5707963267948966], ["1", "2", [3.0, 3.0, 1.0000000000000002], [0.0, -1.0, -2.220446049250313e-16], -1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 4 upwards", "Fold face 3 inwards towards face 5", "Fold face 2 downwards towards face 4", "Fold face 1 downwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net19_base5_step1.png", "output_dir/folding_nets/net19_base5_step2.png", "output_dir/folding_nets/net19_base5_step3.png", "output_dir/folding_nets/net19_base5_step4.png"], "id": "net19_base5"}
2d_perception_color_82_5
What color is face 5 in the cube net shown in the image? <image_0> A. light purple B. yellow C. light green D. light orange
D
color
[ "A. light purple", "B. yellow", "C. light green", "D. light orange" ]
{"initial_net": {"name": "Linear 6-Face Row", "faces": {"1": [[3.0, 0.0, 1.0000000000000002], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [3.0, 1.0, 1.0000000000000002]], "2": [[2.0, 0.0, 1.0], [2.0, 0.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0]], "3": [[2, 0, 0], [3, 0, 0], [3, 1, 0], [2, 1, 0]], "4": [[3.0, 0.0, 0.0], [3.0, 0.0, 1.0], [3.0, 1.0, 1.0], [3.0, 1.0, 0.0]], "5": [[3.0, 0.0, 1.0], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [3.0, 1.0, 1.0]], "6": [[2.0, 0.0, 1.0], [1.9999999999999998, 0.0, 0.0], [1.9999999999999998, 1.0, 0.0], [2.0, 1.0, 1.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": false}, "base_face": "3", "folding_steps": [["4", "3", [3, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "4", [3.0, 0.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "5", [2.0, 0.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["2", "3", [2, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["1", "2", [2.0, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 5 downwards", "Fold face 6 downwards towards face 2", "Fold face 2 upwards towards face 5", "Fold face 1 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net12_base3_step1.png", "output_dir/folding_nets/net12_base3_step2.png", "output_dir/folding_nets/net12_base3_step3.png"], "id": "net12_base3"}
2d_perception_color_82_1
What color is face 1 in the cube net shown in the image? <image_0> A. light blue B. yellow C. light red D. light green
B
color
[ "A. light blue", "B. yellow", "C. light red", "D. light green" ]
{"initial_net": {"name": "Linear 6-Face Row", "faces": {"1": [[3.0, 0.0, 1.0000000000000002], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [3.0, 1.0, 1.0000000000000002]], "2": [[2.0, 0.0, 1.0], [2.0, 0.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0]], "3": [[2, 0, 0], [3, 0, 0], [3, 1, 0], [2, 1, 0]], "4": [[3.0, 0.0, 0.0], [3.0, 0.0, 1.0], [3.0, 1.0, 1.0], [3.0, 1.0, 0.0]], "5": [[3.0, 0.0, 1.0], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [3.0, 1.0, 1.0]], "6": [[2.0, 0.0, 1.0], [1.9999999999999998, 0.0, 0.0], [1.9999999999999998, 1.0, 0.0], [2.0, 1.0, 1.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": false}, "base_face": "3", "folding_steps": [["4", "3", [3, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "4", [3.0, 0.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "5", [2.0, 0.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["2", "3", [2, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["1", "2", [2.0, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 5 downwards", "Fold face 6 downwards towards face 2", "Fold face 2 upwards towards face 5", "Fold face 1 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net12_base3_step1.png", "output_dir/folding_nets/net12_base3_step2.png", "output_dir/folding_nets/net12_base3_step3.png"], "id": "net12_base3"}
2d_perception_connectivity_82_2_6
In the cube net shown in the image, is face 2 directly connected to face 6, yes or no? <image_0>
B
connectivity
[ "Yes", "No" ]
{"initial_net": {"name": "Linear 6-Face Row", "faces": {"1": [[3.0, 0.0, 1.0000000000000002], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [3.0, 1.0, 1.0000000000000002]], "2": [[2.0, 0.0, 1.0], [2.0, 0.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0]], "3": [[2, 0, 0], [3, 0, 0], [3, 1, 0], [2, 1, 0]], "4": [[3.0, 0.0, 0.0], [3.0, 0.0, 1.0], [3.0, 1.0, 1.0], [3.0, 1.0, 0.0]], "5": [[3.0, 0.0, 1.0], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [3.0, 1.0, 1.0]], "6": [[2.0, 0.0, 1.0], [1.9999999999999998, 0.0, 0.0], [1.9999999999999998, 1.0, 0.0], [2.0, 1.0, 1.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": false}, "base_face": "3", "folding_steps": [["4", "3", [3, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "4", [3.0, 0.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "5", [2.0, 0.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["2", "3", [2, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["1", "2", [2.0, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 5 downwards", "Fold face 6 downwards towards face 2", "Fold face 2 upwards towards face 5", "Fold face 1 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net12_base3_step1.png", "output_dir/folding_nets/net12_base3_step2.png", "output_dir/folding_nets/net12_base3_step3.png"], "id": "net12_base3"}
2d_perception_connectivity_82_3_5
In the cube net shown in the image, is face 3 directly connected to face 5, yes or no? <image_0>
A
connectivity
[ "No", "Yes" ]
{"initial_net": {"name": "Linear 6-Face Row", "faces": {"1": [[3.0, 0.0, 1.0000000000000002], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [3.0, 1.0, 1.0000000000000002]], "2": [[2.0, 0.0, 1.0], [2.0, 0.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0]], "3": [[2, 0, 0], [3, 0, 0], [3, 1, 0], [2, 1, 0]], "4": [[3.0, 0.0, 0.0], [3.0, 0.0, 1.0], [3.0, 1.0, 1.0], [3.0, 1.0, 0.0]], "5": [[3.0, 0.0, 1.0], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [3.0, 1.0, 1.0]], "6": [[2.0, 0.0, 1.0], [1.9999999999999998, 0.0, 0.0], [1.9999999999999998, 1.0, 0.0], [2.0, 1.0, 1.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": false}, "base_face": "3", "folding_steps": [["4", "3", [3, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "4", [3.0, 0.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "5", [2.0, 0.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["2", "3", [2, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["1", "2", [2.0, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 5 downwards", "Fold face 6 downwards towards face 2", "Fold face 2 upwards towards face 5", "Fold face 1 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net12_base3_step1.png", "output_dir/folding_nets/net12_base3_step2.png", "output_dir/folding_nets/net12_base3_step3.png"], "id": "net12_base3"}
2d_perception_color_83_3
What color is face 3 in the cube net shown in the image? <image_0> A. light red B. light orange C. light green D. light purple
A
color
[ "A. light red", "B. light orange", "C. light green", "D. light purple" ]
{"initial_net": {"name": "Big T Net", "faces": {"1": [[0.9999999999999999, -0.9999999999999999, 0.0], [1.0, -0.9999999999999999, 1.0], [1.0, -2.0, 1.0], [0.9999999999999999, -2.0, 0.0]], "2": [[1.0, -0.9999999999999999, 1.0], [2.0, -0.9999999999999999, 1.0], [2.0, -2.0, 1.0], [1.0, -2.0, 1.0]], "3": [[2.0, -0.9999999999999999, 1.0], [2.0, -0.9999999999999999, 0.0], [2.0, -2.0, 0.0], [2.0, -2.0, 1.0]], "4": [[1.0, -1.0, 0.0], [2.0, -1.0, 0.0], [2.0, -0.9999999999999999, 1.0], [1.0, -0.9999999999999999, 1.0]], "5": [[1, -2, 0], [2, -2, 0], [2, -1, 0], [1, -1, 0]], "6": [[1.0, -2.0, 1.0], [2.0, -2.0, 1.0], [2.0, -2.0, 0.0], [1.0, -2.0, 0.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3", "4"], "3": ["2"], "4": ["2", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "5", "folding_steps": [["6", "5", [1, -2, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["4", "5", [2, -1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["2", "4", [2.0, -0.9999999999999999, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["1", "2", [1.0, -0.9999999999999999, 1.0], [0.0, -1.0, 0.0], 1.5707963267948966], ["3", "2", [2.0, -0.9999999999999999, 1.0], [0.0, -1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 4 upwards", "Fold face 2 downwards towards face 6", "Fold face 1 downwards towards face 4", "Fold face 3 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net3_base5_step1.png", "output_dir/folding_nets/net3_base5_step2.png", "output_dir/folding_nets/net3_base5_step3.png", "output_dir/folding_nets/net3_base5_step4.png", "output_dir/folding_nets/net3_base5_step5.png", "output_dir/folding_nets/net3_base5_step6.png"], "id": "net3_base5"}
2d_perception_color_83_4
What color is face 4 in the cube net shown in the image? <image_0> A. light red B. light purple C. light blue D. light green
C
color
[ "A. light red", "B. light purple", "C. light blue", "D. light green" ]
{"initial_net": {"name": "Big T Net", "faces": {"1": [[0.9999999999999999, -0.9999999999999999, 0.0], [1.0, -0.9999999999999999, 1.0], [1.0, -2.0, 1.0], [0.9999999999999999, -2.0, 0.0]], "2": [[1.0, -0.9999999999999999, 1.0], [2.0, -0.9999999999999999, 1.0], [2.0, -2.0, 1.0], [1.0, -2.0, 1.0]], "3": [[2.0, -0.9999999999999999, 1.0], [2.0, -0.9999999999999999, 0.0], [2.0, -2.0, 0.0], [2.0, -2.0, 1.0]], "4": [[1.0, -1.0, 0.0], [2.0, -1.0, 0.0], [2.0, -0.9999999999999999, 1.0], [1.0, -0.9999999999999999, 1.0]], "5": [[1, -2, 0], [2, -2, 0], [2, -1, 0], [1, -1, 0]], "6": [[1.0, -2.0, 1.0], [2.0, -2.0, 1.0], [2.0, -2.0, 0.0], [1.0, -2.0, 0.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3", "4"], "3": ["2"], "4": ["2", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "5", "folding_steps": [["6", "5", [1, -2, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["4", "5", [2, -1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["2", "4", [2.0, -0.9999999999999999, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["1", "2", [1.0, -0.9999999999999999, 1.0], [0.0, -1.0, 0.0], 1.5707963267948966], ["3", "2", [2.0, -0.9999999999999999, 1.0], [0.0, -1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 4 upwards", "Fold face 2 downwards towards face 6", "Fold face 1 downwards towards face 4", "Fold face 3 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net3_base5_step1.png", "output_dir/folding_nets/net3_base5_step2.png", "output_dir/folding_nets/net3_base5_step3.png", "output_dir/folding_nets/net3_base5_step4.png", "output_dir/folding_nets/net3_base5_step5.png", "output_dir/folding_nets/net3_base5_step6.png"], "id": "net3_base5"}
2d_perception_connectivity_83_5_6
In the cube net shown in the image, is face 5 directly connected to face 6, yes or no? <image_0>
A
connectivity
[ "Yes", "No" ]
{"initial_net": {"name": "Big T Net", "faces": {"1": [[0.9999999999999999, -0.9999999999999999, 0.0], [1.0, -0.9999999999999999, 1.0], [1.0, -2.0, 1.0], [0.9999999999999999, -2.0, 0.0]], "2": [[1.0, -0.9999999999999999, 1.0], [2.0, -0.9999999999999999, 1.0], [2.0, -2.0, 1.0], [1.0, -2.0, 1.0]], "3": [[2.0, -0.9999999999999999, 1.0], [2.0, -0.9999999999999999, 0.0], [2.0, -2.0, 0.0], [2.0, -2.0, 1.0]], "4": [[1.0, -1.0, 0.0], [2.0, -1.0, 0.0], [2.0, -0.9999999999999999, 1.0], [1.0, -0.9999999999999999, 1.0]], "5": [[1, -2, 0], [2, -2, 0], [2, -1, 0], [1, -1, 0]], "6": [[1.0, -2.0, 1.0], [2.0, -2.0, 1.0], [2.0, -2.0, 0.0], [1.0, -2.0, 0.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3", "4"], "3": ["2"], "4": ["2", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "5", "folding_steps": [["6", "5", [1, -2, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["4", "5", [2, -1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["2", "4", [2.0, -0.9999999999999999, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["1", "2", [1.0, -0.9999999999999999, 1.0], [0.0, -1.0, 0.0], 1.5707963267948966], ["3", "2", [2.0, -0.9999999999999999, 1.0], [0.0, -1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 4 upwards", "Fold face 2 downwards towards face 6", "Fold face 1 downwards towards face 4", "Fold face 3 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net3_base5_step1.png", "output_dir/folding_nets/net3_base5_step2.png", "output_dir/folding_nets/net3_base5_step3.png", "output_dir/folding_nets/net3_base5_step4.png", "output_dir/folding_nets/net3_base5_step5.png", "output_dir/folding_nets/net3_base5_step6.png"], "id": "net3_base5"}
2d_perception_connectivity_83_1_4
In the cube net shown in the image, is face 1 directly connected to face 4, yes or no? <image_0>
A
connectivity
[ "No", "Yes" ]
{"initial_net": {"name": "Big T Net", "faces": {"1": [[0.9999999999999999, -0.9999999999999999, 0.0], [1.0, -0.9999999999999999, 1.0], [1.0, -2.0, 1.0], [0.9999999999999999, -2.0, 0.0]], "2": [[1.0, -0.9999999999999999, 1.0], [2.0, -0.9999999999999999, 1.0], [2.0, -2.0, 1.0], [1.0, -2.0, 1.0]], "3": [[2.0, -0.9999999999999999, 1.0], [2.0, -0.9999999999999999, 0.0], [2.0, -2.0, 0.0], [2.0, -2.0, 1.0]], "4": [[1.0, -1.0, 0.0], [2.0, -1.0, 0.0], [2.0, -0.9999999999999999, 1.0], [1.0, -0.9999999999999999, 1.0]], "5": [[1, -2, 0], [2, -2, 0], [2, -1, 0], [1, -1, 0]], "6": [[1.0, -2.0, 1.0], [2.0, -2.0, 1.0], [2.0, -2.0, 0.0], [1.0, -2.0, 0.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3", "4"], "3": ["2"], "4": ["2", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "5", "folding_steps": [["6", "5", [1, -2, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["4", "5", [2, -1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["2", "4", [2.0, -0.9999999999999999, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["1", "2", [1.0, -0.9999999999999999, 1.0], [0.0, -1.0, 0.0], 1.5707963267948966], ["3", "2", [2.0, -0.9999999999999999, 1.0], [0.0, -1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 4 upwards", "Fold face 2 downwards towards face 6", "Fold face 1 downwards towards face 4", "Fold face 3 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net3_base5_step1.png", "output_dir/folding_nets/net3_base5_step2.png", "output_dir/folding_nets/net3_base5_step3.png", "output_dir/folding_nets/net3_base5_step4.png", "output_dir/folding_nets/net3_base5_step5.png", "output_dir/folding_nets/net3_base5_step6.png"], "id": "net3_base5"}
2d_perception_color_84_4
What color is face 4 in the cube net shown in the image? <image_0> A. light blue B. light red C. yellow D. light green
A
color
[ "A. light blue", "B. light red", "C. yellow", "D. light green" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=4)", "faces": {"4": [[4.0, 1.0, -9.494107596574928e-16], [5.0, 1.0, 0.0], [5.0, 2.0, 0.0], [4.0, 2.0, -9.494107596574928e-16]], "5": [[5.0, 1.0, 0.0], [5.0, 1.0, 1.0], [5.0, 2.0, 1.0], [5.0, 2.0, 0.0]], "3": [[5.0, 1.0, 1.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [5.0, 2.0, 1.0]], "1": [[4.0, 1.0, 1.0], [4.0, 1.0, 0.0], [4.0, 2.0, 0.0], [4.0, 2.0, 1.0]], "6": [[4, 1, 0], [5, 1, 0], [5, 2, 0], [4, 2, 0]], "2": [[4.0, 0.9999999999999999, 1.0], [5.0, 0.9999999999999999, 1.0], [5.0, 1.0, 0.0], [4.0, 1.0, 0.0]]}, "face_connections": {"4": ["5"], "5": ["4", "3"], "3": ["5", "1"], "1": ["3", "6"], "6": ["1", "2"], "2": ["6"]}, "valid": false}, "base_face": "6", "folding_steps": [["1", "6", [4, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "1", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "3", [5.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "5", [5.0, 1.0, 0.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "6", [4, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 3 downwards", "Fold face 5 downwards towards face 6", "Fold face 4 upwards towards face 1", "Fold face 2 upwards towards face 4"], "images_per_step": ["output_dir/folding_nets/random1_net17_base6_step1.png", "output_dir/folding_nets/random1_net17_base6_step2.png", "output_dir/folding_nets/random1_net17_base6_step3.png", "output_dir/folding_nets/random1_net17_base6_step4.png"], "id": "random1_net17_base6"}
2d_perception_color_84_6
What color is face 6 in the cube net shown in the image? <image_0> A. light blue B. light orange C. light purple D. light green
D
color
[ "A. light blue", "B. light orange", "C. light purple", "D. light green" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=4)", "faces": {"4": [[4.0, 1.0, -9.494107596574928e-16], [5.0, 1.0, 0.0], [5.0, 2.0, 0.0], [4.0, 2.0, -9.494107596574928e-16]], "5": [[5.0, 1.0, 0.0], [5.0, 1.0, 1.0], [5.0, 2.0, 1.0], [5.0, 2.0, 0.0]], "3": [[5.0, 1.0, 1.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [5.0, 2.0, 1.0]], "1": [[4.0, 1.0, 1.0], [4.0, 1.0, 0.0], [4.0, 2.0, 0.0], [4.0, 2.0, 1.0]], "6": [[4, 1, 0], [5, 1, 0], [5, 2, 0], [4, 2, 0]], "2": [[4.0, 0.9999999999999999, 1.0], [5.0, 0.9999999999999999, 1.0], [5.0, 1.0, 0.0], [4.0, 1.0, 0.0]]}, "face_connections": {"4": ["5"], "5": ["4", "3"], "3": ["5", "1"], "1": ["3", "6"], "6": ["1", "2"], "2": ["6"]}, "valid": false}, "base_face": "6", "folding_steps": [["1", "6", [4, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "1", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "3", [5.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "5", [5.0, 1.0, 0.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "6", [4, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 3 downwards", "Fold face 5 downwards towards face 6", "Fold face 4 upwards towards face 1", "Fold face 2 upwards towards face 4"], "images_per_step": ["output_dir/folding_nets/random1_net17_base6_step1.png", "output_dir/folding_nets/random1_net17_base6_step2.png", "output_dir/folding_nets/random1_net17_base6_step3.png", "output_dir/folding_nets/random1_net17_base6_step4.png"], "id": "random1_net17_base6"}
2d_perception_connectivity_84_1_2
In the cube net shown in the image, is face 1 directly connected to face 2, yes or no? <image_0>
A
connectivity
[ "No", "Yes" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=4)", "faces": {"4": [[4.0, 1.0, -9.494107596574928e-16], [5.0, 1.0, 0.0], [5.0, 2.0, 0.0], [4.0, 2.0, -9.494107596574928e-16]], "5": [[5.0, 1.0, 0.0], [5.0, 1.0, 1.0], [5.0, 2.0, 1.0], [5.0, 2.0, 0.0]], "3": [[5.0, 1.0, 1.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [5.0, 2.0, 1.0]], "1": [[4.0, 1.0, 1.0], [4.0, 1.0, 0.0], [4.0, 2.0, 0.0], [4.0, 2.0, 1.0]], "6": [[4, 1, 0], [5, 1, 0], [5, 2, 0], [4, 2, 0]], "2": [[4.0, 0.9999999999999999, 1.0], [5.0, 0.9999999999999999, 1.0], [5.0, 1.0, 0.0], [4.0, 1.0, 0.0]]}, "face_connections": {"4": ["5"], "5": ["4", "3"], "3": ["5", "1"], "1": ["3", "6"], "6": ["1", "2"], "2": ["6"]}, "valid": false}, "base_face": "6", "folding_steps": [["1", "6", [4, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "1", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "3", [5.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "5", [5.0, 1.0, 0.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "6", [4, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 3 downwards", "Fold face 5 downwards towards face 6", "Fold face 4 upwards towards face 1", "Fold face 2 upwards towards face 4"], "images_per_step": ["output_dir/folding_nets/random1_net17_base6_step1.png", "output_dir/folding_nets/random1_net17_base6_step2.png", "output_dir/folding_nets/random1_net17_base6_step3.png", "output_dir/folding_nets/random1_net17_base6_step4.png"], "id": "random1_net17_base6"}
2d_perception_connectivity_84_3_2
In the cube net shown in the image, is face 3 directly connected to face 2, yes or no? <image_0>
B
connectivity
[ "Yes", "No" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=4)", "faces": {"4": [[4.0, 1.0, -9.494107596574928e-16], [5.0, 1.0, 0.0], [5.0, 2.0, 0.0], [4.0, 2.0, -9.494107596574928e-16]], "5": [[5.0, 1.0, 0.0], [5.0, 1.0, 1.0], [5.0, 2.0, 1.0], [5.0, 2.0, 0.0]], "3": [[5.0, 1.0, 1.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [5.0, 2.0, 1.0]], "1": [[4.0, 1.0, 1.0], [4.0, 1.0, 0.0], [4.0, 2.0, 0.0], [4.0, 2.0, 1.0]], "6": [[4, 1, 0], [5, 1, 0], [5, 2, 0], [4, 2, 0]], "2": [[4.0, 0.9999999999999999, 1.0], [5.0, 0.9999999999999999, 1.0], [5.0, 1.0, 0.0], [4.0, 1.0, 0.0]]}, "face_connections": {"4": ["5"], "5": ["4", "3"], "3": ["5", "1"], "1": ["3", "6"], "6": ["1", "2"], "2": ["6"]}, "valid": false}, "base_face": "6", "folding_steps": [["1", "6", [4, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "1", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "3", [5.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["4", "5", [5.0, 1.0, 0.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "6", [4, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 3 downwards", "Fold face 5 downwards towards face 6", "Fold face 4 upwards towards face 1", "Fold face 2 upwards towards face 4"], "images_per_step": ["output_dir/folding_nets/random1_net17_base6_step1.png", "output_dir/folding_nets/random1_net17_base6_step2.png", "output_dir/folding_nets/random1_net17_base6_step3.png", "output_dir/folding_nets/random1_net17_base6_step4.png"], "id": "random1_net17_base6"}
2d_perception_color_85_4
What color is face 4 in the cube net shown in the image? <image_0> A. yellow B. light green C. light blue D. light orange
C
color
[ "A. yellow", "B. light green", "C. light blue", "D. light orange" ]
{"initial_net": {"name": "t-shaped Net Variant 2", "faces": {"3": [[0.9999999999999999, 0.0, 1.0], [1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, 1.0]], "2": [[2.0, 0.0, 1.0], [0.9999999999999999, 0.0, 1.0], [0.9999999999999999, 1.0, 1.0], [2.0, 1.0, 1.0]], "4": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "5": [[2.0, 0.0, 0.0], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]], "6": [[2.0, -6.123233995736766e-17, 1.0], [2.0, -6.123233995736766e-17, 1.1102230246251565e-16], [1.0, 0.0, 0.0], [0.9999999999999999, 0.0, 1.0]], "1": [[2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 0.0]]}, "face_connections": {"1": ["5"], "2": ["3"], "3": ["2", "4", "6"], "4": ["3", "5"], "5": ["1", "4"], "6": ["3"]}, "valid": true}, "base_face": "4", "folding_steps": [["3", "4", [1, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "4", [2, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "3", [0.9999999999999999, 0.0, 1.0], [1.1102230246251565e-16, 0.0, -1.0], -1.5707963267948966], ["1", "5", [2.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["2", "3", [0.9999999999999999, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 5 upwards", "Fold face 6 inwards towards face 4", "Fold face 1 inwards towards face 3", "Fold face 2 downwards towards face 5"], "images_per_step": ["output_dir/folding_nets/net2_base4_step1.png", "output_dir/folding_nets/net2_base4_step2.png", "output_dir/folding_nets/net2_base4_step3.png", "output_dir/folding_nets/net2_base4_step4.png", "output_dir/folding_nets/net2_base4_step5.png", "output_dir/folding_nets/net2_base4_step6.png"], "id": "net2_base4"}
2d_perception_color_85_6
What color is face 6 in the cube net shown in the image? <image_0> A. light green B. light orange C. light blue D. light red
A
color
[ "A. light green", "B. light orange", "C. light blue", "D. light red" ]
{"initial_net": {"name": "t-shaped Net Variant 2", "faces": {"3": [[0.9999999999999999, 0.0, 1.0], [1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, 1.0]], "2": [[2.0, 0.0, 1.0], [0.9999999999999999, 0.0, 1.0], [0.9999999999999999, 1.0, 1.0], [2.0, 1.0, 1.0]], "4": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "5": [[2.0, 0.0, 0.0], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]], "6": [[2.0, -6.123233995736766e-17, 1.0], [2.0, -6.123233995736766e-17, 1.1102230246251565e-16], [1.0, 0.0, 0.0], [0.9999999999999999, 0.0, 1.0]], "1": [[2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 0.0]]}, "face_connections": {"1": ["5"], "2": ["3"], "3": ["2", "4", "6"], "4": ["3", "5"], "5": ["1", "4"], "6": ["3"]}, "valid": true}, "base_face": "4", "folding_steps": [["3", "4", [1, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "4", [2, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "3", [0.9999999999999999, 0.0, 1.0], [1.1102230246251565e-16, 0.0, -1.0], -1.5707963267948966], ["1", "5", [2.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["2", "3", [0.9999999999999999, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 5 upwards", "Fold face 6 inwards towards face 4", "Fold face 1 inwards towards face 3", "Fold face 2 downwards towards face 5"], "images_per_step": ["output_dir/folding_nets/net2_base4_step1.png", "output_dir/folding_nets/net2_base4_step2.png", "output_dir/folding_nets/net2_base4_step3.png", "output_dir/folding_nets/net2_base4_step4.png", "output_dir/folding_nets/net2_base4_step5.png", "output_dir/folding_nets/net2_base4_step6.png"], "id": "net2_base4"}
2d_perception_connectivity_85_2_1
In the cube net shown in the image, is face 2 directly connected to face 1, yes or no? <image_0>
A
connectivity
[ "No", "Yes" ]
{"initial_net": {"name": "t-shaped Net Variant 2", "faces": {"3": [[0.9999999999999999, 0.0, 1.0], [1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, 1.0]], "2": [[2.0, 0.0, 1.0], [0.9999999999999999, 0.0, 1.0], [0.9999999999999999, 1.0, 1.0], [2.0, 1.0, 1.0]], "4": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "5": [[2.0, 0.0, 0.0], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]], "6": [[2.0, -6.123233995736766e-17, 1.0], [2.0, -6.123233995736766e-17, 1.1102230246251565e-16], [1.0, 0.0, 0.0], [0.9999999999999999, 0.0, 1.0]], "1": [[2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 0.0]]}, "face_connections": {"1": ["5"], "2": ["3"], "3": ["2", "4", "6"], "4": ["3", "5"], "5": ["1", "4"], "6": ["3"]}, "valid": true}, "base_face": "4", "folding_steps": [["3", "4", [1, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "4", [2, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "3", [0.9999999999999999, 0.0, 1.0], [1.1102230246251565e-16, 0.0, -1.0], -1.5707963267948966], ["1", "5", [2.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["2", "3", [0.9999999999999999, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 5 upwards", "Fold face 6 inwards towards face 4", "Fold face 1 inwards towards face 3", "Fold face 2 downwards towards face 5"], "images_per_step": ["output_dir/folding_nets/net2_base4_step1.png", "output_dir/folding_nets/net2_base4_step2.png", "output_dir/folding_nets/net2_base4_step3.png", "output_dir/folding_nets/net2_base4_step4.png", "output_dir/folding_nets/net2_base4_step5.png", "output_dir/folding_nets/net2_base4_step6.png"], "id": "net2_base4"}
2d_perception_connectivity_85_3_5
In the cube net shown in the image, is face 3 directly connected to face 5, yes or no? <image_0>
A
connectivity
[ "No", "Yes" ]
{"initial_net": {"name": "t-shaped Net Variant 2", "faces": {"3": [[0.9999999999999999, 0.0, 1.0], [1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, 1.0]], "2": [[2.0, 0.0, 1.0], [0.9999999999999999, 0.0, 1.0], [0.9999999999999999, 1.0, 1.0], [2.0, 1.0, 1.0]], "4": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "5": [[2.0, 0.0, 0.0], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]], "6": [[2.0, -6.123233995736766e-17, 1.0], [2.0, -6.123233995736766e-17, 1.1102230246251565e-16], [1.0, 0.0, 0.0], [0.9999999999999999, 0.0, 1.0]], "1": [[2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 0.0]]}, "face_connections": {"1": ["5"], "2": ["3"], "3": ["2", "4", "6"], "4": ["3", "5"], "5": ["1", "4"], "6": ["3"]}, "valid": true}, "base_face": "4", "folding_steps": [["3", "4", [1, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "4", [2, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "3", [0.9999999999999999, 0.0, 1.0], [1.1102230246251565e-16, 0.0, -1.0], -1.5707963267948966], ["1", "5", [2.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["2", "3", [0.9999999999999999, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 5 upwards", "Fold face 6 inwards towards face 4", "Fold face 1 inwards towards face 3", "Fold face 2 downwards towards face 5"], "images_per_step": ["output_dir/folding_nets/net2_base4_step1.png", "output_dir/folding_nets/net2_base4_step2.png", "output_dir/folding_nets/net2_base4_step3.png", "output_dir/folding_nets/net2_base4_step4.png", "output_dir/folding_nets/net2_base4_step5.png", "output_dir/folding_nets/net2_base4_step6.png"], "id": "net2_base4"}
2d_perception_color_86_4
What color is face 4 in the cube net shown in the image? <image_0> A. yellow B. light blue C. light green D. light red
B
color
[ "A. yellow", "B. light blue", "C. light green", "D. light red" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=3)", "faces": {"4": [[0, 1, 0], [1, 1, 0], [1, 2, 0], [0, 2, 0]], "2": [[1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0]], "5": [[1.0, 1.0, 1.0], [0.0, 1.0, 1.0000000000000002], [0.0, 2.0, 1.0000000000000002], [1.0, 2.0, 1.0]], "6": [[0.0, 1.0, 1.0000000000000002], [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [-2.83276944882399e-16, 2.0, 2.220446049250313e-16], [0.0, 2.0, 1.0000000000000002]], "1": [[-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.9999999999999997, 1.0, 9.957992501029596e-17], [0.9999999999999997, 2.0, 9.957992501029596e-17], [-2.83276944882399e-16, 2.0, 2.220446049250313e-16]], "3": [[1.0, 0.9999999999999999, 0.9999999999999999], [0.9999999999999997, 0.9999999999999999, 0.0], [-2.8327694488239893e-16, 1.0, 2.220446049250313e-16], [0.0, 1.0, 1.0000000000000002]]}, "face_connections": {"4": ["2"], "2": ["4", "5"], "5": ["2", "6"], "6": ["5", "1", "3"], "1": ["6"], "3": ["6"]}, "valid": false}, "base_face": "4", "folding_steps": [["2", "4", [1, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "2", [1.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "5", [0.0, 1.0, 1.0000000000000002], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "6", [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "6", [0.0, 1.0, 1.0000000000000002], [-2.83276944882399e-16, 0.0, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 5 downwards", "Fold face 6 downwards towards face 4", "Fold face 1 upwards towards face 4", "Fold face 3 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/random3_net16_base4_step1.png", "output_dir/folding_nets/random3_net16_base4_step2.png", "output_dir/folding_nets/random3_net16_base4_step3.png"], "id": "random3_net16_base4"}
2d_perception_color_86_3
What color is face 3 in the cube net shown in the image? <image_0> A. light purple B. light orange C. light red D. light blue
C
color
[ "A. light purple", "B. light orange", "C. light red", "D. light blue" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=3)", "faces": {"4": [[0, 1, 0], [1, 1, 0], [1, 2, 0], [0, 2, 0]], "2": [[1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0]], "5": [[1.0, 1.0, 1.0], [0.0, 1.0, 1.0000000000000002], [0.0, 2.0, 1.0000000000000002], [1.0, 2.0, 1.0]], "6": [[0.0, 1.0, 1.0000000000000002], [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [-2.83276944882399e-16, 2.0, 2.220446049250313e-16], [0.0, 2.0, 1.0000000000000002]], "1": [[-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.9999999999999997, 1.0, 9.957992501029596e-17], [0.9999999999999997, 2.0, 9.957992501029596e-17], [-2.83276944882399e-16, 2.0, 2.220446049250313e-16]], "3": [[1.0, 0.9999999999999999, 0.9999999999999999], [0.9999999999999997, 0.9999999999999999, 0.0], [-2.8327694488239893e-16, 1.0, 2.220446049250313e-16], [0.0, 1.0, 1.0000000000000002]]}, "face_connections": {"4": ["2"], "2": ["4", "5"], "5": ["2", "6"], "6": ["5", "1", "3"], "1": ["6"], "3": ["6"]}, "valid": false}, "base_face": "4", "folding_steps": [["2", "4", [1, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "2", [1.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "5", [0.0, 1.0, 1.0000000000000002], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "6", [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "6", [0.0, 1.0, 1.0000000000000002], [-2.83276944882399e-16, 0.0, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 5 downwards", "Fold face 6 downwards towards face 4", "Fold face 1 upwards towards face 4", "Fold face 3 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/random3_net16_base4_step1.png", "output_dir/folding_nets/random3_net16_base4_step2.png", "output_dir/folding_nets/random3_net16_base4_step3.png"], "id": "random3_net16_base4"}
2d_perception_connectivity_86_4_2
In the cube net shown in the image, is face 4 directly connected to face 2, yes or no? <image_0>
B
connectivity
[ "No", "Yes" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=3)", "faces": {"4": [[0, 1, 0], [1, 1, 0], [1, 2, 0], [0, 2, 0]], "2": [[1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0]], "5": [[1.0, 1.0, 1.0], [0.0, 1.0, 1.0000000000000002], [0.0, 2.0, 1.0000000000000002], [1.0, 2.0, 1.0]], "6": [[0.0, 1.0, 1.0000000000000002], [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [-2.83276944882399e-16, 2.0, 2.220446049250313e-16], [0.0, 2.0, 1.0000000000000002]], "1": [[-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.9999999999999997, 1.0, 9.957992501029596e-17], [0.9999999999999997, 2.0, 9.957992501029596e-17], [-2.83276944882399e-16, 2.0, 2.220446049250313e-16]], "3": [[1.0, 0.9999999999999999, 0.9999999999999999], [0.9999999999999997, 0.9999999999999999, 0.0], [-2.8327694488239893e-16, 1.0, 2.220446049250313e-16], [0.0, 1.0, 1.0000000000000002]]}, "face_connections": {"4": ["2"], "2": ["4", "5"], "5": ["2", "6"], "6": ["5", "1", "3"], "1": ["6"], "3": ["6"]}, "valid": false}, "base_face": "4", "folding_steps": [["2", "4", [1, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "2", [1.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "5", [0.0, 1.0, 1.0000000000000002], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "6", [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "6", [0.0, 1.0, 1.0000000000000002], [-2.83276944882399e-16, 0.0, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 5 downwards", "Fold face 6 downwards towards face 4", "Fold face 1 upwards towards face 4", "Fold face 3 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/random3_net16_base4_step1.png", "output_dir/folding_nets/random3_net16_base4_step2.png", "output_dir/folding_nets/random3_net16_base4_step3.png"], "id": "random3_net16_base4"}
2d_perception_connectivity_86_5_3
In the cube net shown in the image, is face 5 directly connected to face 3, yes or no? <image_0>
A
connectivity
[ "No", "Yes" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=3)", "faces": {"4": [[0, 1, 0], [1, 1, 0], [1, 2, 0], [0, 2, 0]], "2": [[1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0]], "5": [[1.0, 1.0, 1.0], [0.0, 1.0, 1.0000000000000002], [0.0, 2.0, 1.0000000000000002], [1.0, 2.0, 1.0]], "6": [[0.0, 1.0, 1.0000000000000002], [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [-2.83276944882399e-16, 2.0, 2.220446049250313e-16], [0.0, 2.0, 1.0000000000000002]], "1": [[-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.9999999999999997, 1.0, 9.957992501029596e-17], [0.9999999999999997, 2.0, 9.957992501029596e-17], [-2.83276944882399e-16, 2.0, 2.220446049250313e-16]], "3": [[1.0, 0.9999999999999999, 0.9999999999999999], [0.9999999999999997, 0.9999999999999999, 0.0], [-2.8327694488239893e-16, 1.0, 2.220446049250313e-16], [0.0, 1.0, 1.0000000000000002]]}, "face_connections": {"4": ["2"], "2": ["4", "5"], "5": ["2", "6"], "6": ["5", "1", "3"], "1": ["6"], "3": ["6"]}, "valid": false}, "base_face": "4", "folding_steps": [["2", "4", [1, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "2", [1.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "5", [0.0, 1.0, 1.0000000000000002], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "6", [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "6", [0.0, 1.0, 1.0000000000000002], [-2.83276944882399e-16, 0.0, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 5 downwards", "Fold face 6 downwards towards face 4", "Fold face 1 upwards towards face 4", "Fold face 3 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/random3_net16_base4_step1.png", "output_dir/folding_nets/random3_net16_base4_step2.png", "output_dir/folding_nets/random3_net16_base4_step3.png"], "id": "random3_net16_base4"}
2d_perception_color_87_5
What color is face 5 in the cube net shown in the image? <image_0> A. light orange B. light red C. light blue D. light green
A
color
[ "A. light orange", "B. light red", "C. light blue", "D. light green" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=1)", "faces": {"6": [[4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [4.0, 2.0, 0.0]], "5": [[4.0, 1.0, 1.0], [3.0, 1.0, 1.0], [3.0, 2.0, 1.0], [4.0, 2.0, 1.0]], "4": [[3.0, 1.0, 1.0], [3.0, 1.0, 0.0], [3.0, 2.0, 0.0], [3.0, 2.0, 1.0]], "3": [[3, 1, 0], [4, 1, 0], [4, 2, 0], [3, 2, 0]], "1": [[4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [4.0, 2.0, 0.0]], "2": [[4.0, 0.9999999999999999, 0.0], [3.0, 0.9999999999999999, 0.0], [3.0, 1.0, 1.0], [4.0, 1.0, 1.0]]}, "face_connections": {"6": ["5"], "5": ["6", "4", "2"], "4": ["5", "3"], "3": ["4", "1"], "1": ["3"], "2": ["5"]}, "valid": false}, "base_face": "3", "folding_steps": [["1", "3", [4, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "3", [3, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "4", [3.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "5", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "5", [4.0, 1.0, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 4 upwards", "Fold face 5 downwards towards face 1", "Fold face 6 downwards towards face 3", "Fold face 2 downwards towards face 6"], "images_per_step": ["output_dir/folding_nets/random3_net14_base3_step1.png", "output_dir/folding_nets/random3_net14_base3_step2.png", "output_dir/folding_nets/random3_net14_base3_step3.png"], "id": "random3_net14_base3"}
2d_perception_color_87_1
What color is face 1 in the cube net shown in the image? <image_0> A. yellow B. light red C. light blue D. light green
A
color
[ "A. yellow", "B. light red", "C. light blue", "D. light green" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=1)", "faces": {"6": [[4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [4.0, 2.0, 0.0]], "5": [[4.0, 1.0, 1.0], [3.0, 1.0, 1.0], [3.0, 2.0, 1.0], [4.0, 2.0, 1.0]], "4": [[3.0, 1.0, 1.0], [3.0, 1.0, 0.0], [3.0, 2.0, 0.0], [3.0, 2.0, 1.0]], "3": [[3, 1, 0], [4, 1, 0], [4, 2, 0], [3, 2, 0]], "1": [[4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [4.0, 2.0, 0.0]], "2": [[4.0, 0.9999999999999999, 0.0], [3.0, 0.9999999999999999, 0.0], [3.0, 1.0, 1.0], [4.0, 1.0, 1.0]]}, "face_connections": {"6": ["5"], "5": ["6", "4", "2"], "4": ["5", "3"], "3": ["4", "1"], "1": ["3"], "2": ["5"]}, "valid": false}, "base_face": "3", "folding_steps": [["1", "3", [4, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "3", [3, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "4", [3.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "5", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "5", [4.0, 1.0, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 4 upwards", "Fold face 5 downwards towards face 1", "Fold face 6 downwards towards face 3", "Fold face 2 downwards towards face 6"], "images_per_step": ["output_dir/folding_nets/random3_net14_base3_step1.png", "output_dir/folding_nets/random3_net14_base3_step2.png", "output_dir/folding_nets/random3_net14_base3_step3.png"], "id": "random3_net14_base3"}
2d_perception_connectivity_87_4_3
In the cube net shown in the image, is face 4 directly connected to face 3, yes or no? <image_0>
A
connectivity
[ "Yes", "No" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=1)", "faces": {"6": [[4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [4.0, 2.0, 0.0]], "5": [[4.0, 1.0, 1.0], [3.0, 1.0, 1.0], [3.0, 2.0, 1.0], [4.0, 2.0, 1.0]], "4": [[3.0, 1.0, 1.0], [3.0, 1.0, 0.0], [3.0, 2.0, 0.0], [3.0, 2.0, 1.0]], "3": [[3, 1, 0], [4, 1, 0], [4, 2, 0], [3, 2, 0]], "1": [[4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [4.0, 2.0, 0.0]], "2": [[4.0, 0.9999999999999999, 0.0], [3.0, 0.9999999999999999, 0.0], [3.0, 1.0, 1.0], [4.0, 1.0, 1.0]]}, "face_connections": {"6": ["5"], "5": ["6", "4", "2"], "4": ["5", "3"], "3": ["4", "1"], "1": ["3"], "2": ["5"]}, "valid": false}, "base_face": "3", "folding_steps": [["1", "3", [4, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "3", [3, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "4", [3.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "5", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "5", [4.0, 1.0, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 4 upwards", "Fold face 5 downwards towards face 1", "Fold face 6 downwards towards face 3", "Fold face 2 downwards towards face 6"], "images_per_step": ["output_dir/folding_nets/random3_net14_base3_step1.png", "output_dir/folding_nets/random3_net14_base3_step2.png", "output_dir/folding_nets/random3_net14_base3_step3.png"], "id": "random3_net14_base3"}
2d_perception_connectivity_87_1_2
In the cube net shown in the image, is face 1 directly connected to face 2, yes or no? <image_0>
B
connectivity
[ "Yes", "No" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=1)", "faces": {"6": [[4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [4.0, 2.0, 0.0]], "5": [[4.0, 1.0, 1.0], [3.0, 1.0, 1.0], [3.0, 2.0, 1.0], [4.0, 2.0, 1.0]], "4": [[3.0, 1.0, 1.0], [3.0, 1.0, 0.0], [3.0, 2.0, 0.0], [3.0, 2.0, 1.0]], "3": [[3, 1, 0], [4, 1, 0], [4, 2, 0], [3, 2, 0]], "1": [[4.0, 1.0, 0.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [4.0, 2.0, 0.0]], "2": [[4.0, 0.9999999999999999, 0.0], [3.0, 0.9999999999999999, 0.0], [3.0, 1.0, 1.0], [4.0, 1.0, 1.0]]}, "face_connections": {"6": ["5"], "5": ["6", "4", "2"], "4": ["5", "3"], "3": ["4", "1"], "1": ["3"], "2": ["5"]}, "valid": false}, "base_face": "3", "folding_steps": [["1", "3", [4, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "3", [3, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["5", "4", [3.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "5", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "5", [4.0, 1.0, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 4 upwards", "Fold face 5 downwards towards face 1", "Fold face 6 downwards towards face 3", "Fold face 2 downwards towards face 6"], "images_per_step": ["output_dir/folding_nets/random3_net14_base3_step1.png", "output_dir/folding_nets/random3_net14_base3_step2.png", "output_dir/folding_nets/random3_net14_base3_step3.png"], "id": "random3_net14_base3"}
2d_perception_color_88_6
What color is face 6 in the cube net shown in the image? <image_0> A. light orange B. light green C. light blue D. yellow
B
color
[ "A. light orange", "B. light green", "C. light blue", "D. yellow" ]
{"initial_net": {"name": "1-3-2 Net", "faces": {"1": [[0.9999999999999999, 2.0, 1.0], [1.0, 0.9999999999999999, 1.0], [1.0, 1.0, 0.0], [0.9999999999999999, 2.0, 1.1102230246251565e-16]], "2": [[1.0, 2.0, 0.0], [2.0, 2.0, 0.0], [2.0, 2.0, 1.0], [1.0, 2.0, 1.0]], "3": [[1, 1, 0], [2, 1, 0], [2, 2, 0], [1, 2, 0]], "4": [[1.0, 0.9999999999999999, 1.0], [2.0, 0.9999999999999999, 1.0], [2.0, 1.0, 0.0], [1.0, 1.0, 0.0]], "5": [[2.0, 0.9999999999999999, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 1.1102230246251565e-16], [2.0, 1.0, 0.0]], "6": [[1.0, 0.9999999999999998, 1.0], [1.0, 1.9999999999999998, 1.0], [2.0, 2.0, 1.0], [2.0, 0.9999999999999999, 1.0]]}, "face_connections": {"1": ["4"], "2": ["3"], "3": ["2", "4"], "4": ["1", "3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "3", "folding_steps": [["4", "3", [1, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["5", "4", [2.0, 0.9999999999999999, 1.0], [0.0, 1.1102230246251565e-16, -1.0], -1.5707963267948966], ["6", "5", [2.0, 0.9999999999999999, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "4", [1.0, 0.9999999999999999, 1.0], [0.0, 1.1102230246251565e-16, -1.0], 1.5707963267948966], ["2", "3", [2, 2, 0], [-1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 5 inwards towards face 3", "Fold face 6 downwards towards face 4", "Fold face 1 inwards towards face 3", "Fold face 2 upwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net11_base3_step1.png", "output_dir/folding_nets/net11_base3_step2.png", "output_dir/folding_nets/net11_base3_step3.png", "output_dir/folding_nets/net11_base3_step4.png", "output_dir/folding_nets/net11_base3_step5.png", "output_dir/folding_nets/net11_base3_step6.png"], "id": "net11_base3"}
2d_perception_color_88_3
What color is face 3 in the cube net shown in the image? <image_0> A. light purple B. light blue C. light green D. light red
D
color
[ "A. light purple", "B. light blue", "C. light green", "D. light red" ]
{"initial_net": {"name": "1-3-2 Net", "faces": {"1": [[0.9999999999999999, 2.0, 1.0], [1.0, 0.9999999999999999, 1.0], [1.0, 1.0, 0.0], [0.9999999999999999, 2.0, 1.1102230246251565e-16]], "2": [[1.0, 2.0, 0.0], [2.0, 2.0, 0.0], [2.0, 2.0, 1.0], [1.0, 2.0, 1.0]], "3": [[1, 1, 0], [2, 1, 0], [2, 2, 0], [1, 2, 0]], "4": [[1.0, 0.9999999999999999, 1.0], [2.0, 0.9999999999999999, 1.0], [2.0, 1.0, 0.0], [1.0, 1.0, 0.0]], "5": [[2.0, 0.9999999999999999, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 1.1102230246251565e-16], [2.0, 1.0, 0.0]], "6": [[1.0, 0.9999999999999998, 1.0], [1.0, 1.9999999999999998, 1.0], [2.0, 2.0, 1.0], [2.0, 0.9999999999999999, 1.0]]}, "face_connections": {"1": ["4"], "2": ["3"], "3": ["2", "4"], "4": ["1", "3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "3", "folding_steps": [["4", "3", [1, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["5", "4", [2.0, 0.9999999999999999, 1.0], [0.0, 1.1102230246251565e-16, -1.0], -1.5707963267948966], ["6", "5", [2.0, 0.9999999999999999, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "4", [1.0, 0.9999999999999999, 1.0], [0.0, 1.1102230246251565e-16, -1.0], 1.5707963267948966], ["2", "3", [2, 2, 0], [-1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 5 inwards towards face 3", "Fold face 6 downwards towards face 4", "Fold face 1 inwards towards face 3", "Fold face 2 upwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net11_base3_step1.png", "output_dir/folding_nets/net11_base3_step2.png", "output_dir/folding_nets/net11_base3_step3.png", "output_dir/folding_nets/net11_base3_step4.png", "output_dir/folding_nets/net11_base3_step5.png", "output_dir/folding_nets/net11_base3_step6.png"], "id": "net11_base3"}
2d_perception_connectivity_88_2_5
In the cube net shown in the image, is face 2 directly connected to face 5, yes or no? <image_0>
A
connectivity
[ "No", "Yes" ]
{"initial_net": {"name": "1-3-2 Net", "faces": {"1": [[0.9999999999999999, 2.0, 1.0], [1.0, 0.9999999999999999, 1.0], [1.0, 1.0, 0.0], [0.9999999999999999, 2.0, 1.1102230246251565e-16]], "2": [[1.0, 2.0, 0.0], [2.0, 2.0, 0.0], [2.0, 2.0, 1.0], [1.0, 2.0, 1.0]], "3": [[1, 1, 0], [2, 1, 0], [2, 2, 0], [1, 2, 0]], "4": [[1.0, 0.9999999999999999, 1.0], [2.0, 0.9999999999999999, 1.0], [2.0, 1.0, 0.0], [1.0, 1.0, 0.0]], "5": [[2.0, 0.9999999999999999, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 1.1102230246251565e-16], [2.0, 1.0, 0.0]], "6": [[1.0, 0.9999999999999998, 1.0], [1.0, 1.9999999999999998, 1.0], [2.0, 2.0, 1.0], [2.0, 0.9999999999999999, 1.0]]}, "face_connections": {"1": ["4"], "2": ["3"], "3": ["2", "4"], "4": ["1", "3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "3", "folding_steps": [["4", "3", [1, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["5", "4", [2.0, 0.9999999999999999, 1.0], [0.0, 1.1102230246251565e-16, -1.0], -1.5707963267948966], ["6", "5", [2.0, 0.9999999999999999, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "4", [1.0, 0.9999999999999999, 1.0], [0.0, 1.1102230246251565e-16, -1.0], 1.5707963267948966], ["2", "3", [2, 2, 0], [-1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 5 inwards towards face 3", "Fold face 6 downwards towards face 4", "Fold face 1 inwards towards face 3", "Fold face 2 upwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net11_base3_step1.png", "output_dir/folding_nets/net11_base3_step2.png", "output_dir/folding_nets/net11_base3_step3.png", "output_dir/folding_nets/net11_base3_step4.png", "output_dir/folding_nets/net11_base3_step5.png", "output_dir/folding_nets/net11_base3_step6.png"], "id": "net11_base3"}
2d_perception_connectivity_88_2_6
In the cube net shown in the image, is face 2 directly connected to face 6, yes or no? <image_0>
B
connectivity
[ "Yes", "No" ]
{"initial_net": {"name": "1-3-2 Net", "faces": {"1": [[0.9999999999999999, 2.0, 1.0], [1.0, 0.9999999999999999, 1.0], [1.0, 1.0, 0.0], [0.9999999999999999, 2.0, 1.1102230246251565e-16]], "2": [[1.0, 2.0, 0.0], [2.0, 2.0, 0.0], [2.0, 2.0, 1.0], [1.0, 2.0, 1.0]], "3": [[1, 1, 0], [2, 1, 0], [2, 2, 0], [1, 2, 0]], "4": [[1.0, 0.9999999999999999, 1.0], [2.0, 0.9999999999999999, 1.0], [2.0, 1.0, 0.0], [1.0, 1.0, 0.0]], "5": [[2.0, 0.9999999999999999, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 1.1102230246251565e-16], [2.0, 1.0, 0.0]], "6": [[1.0, 0.9999999999999998, 1.0], [1.0, 1.9999999999999998, 1.0], [2.0, 2.0, 1.0], [2.0, 0.9999999999999999, 1.0]]}, "face_connections": {"1": ["4"], "2": ["3"], "3": ["2", "4"], "4": ["1", "3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "3", "folding_steps": [["4", "3", [1, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["5", "4", [2.0, 0.9999999999999999, 1.0], [0.0, 1.1102230246251565e-16, -1.0], -1.5707963267948966], ["6", "5", [2.0, 0.9999999999999999, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "4", [1.0, 0.9999999999999999, 1.0], [0.0, 1.1102230246251565e-16, -1.0], 1.5707963267948966], ["2", "3", [2, 2, 0], [-1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 5 inwards towards face 3", "Fold face 6 downwards towards face 4", "Fold face 1 inwards towards face 3", "Fold face 2 upwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net11_base3_step1.png", "output_dir/folding_nets/net11_base3_step2.png", "output_dir/folding_nets/net11_base3_step3.png", "output_dir/folding_nets/net11_base3_step4.png", "output_dir/folding_nets/net11_base3_step5.png", "output_dir/folding_nets/net11_base3_step6.png"], "id": "net11_base3"}
2d_perception_color_89_1
What color is face 1 in the cube net shown in the image? <image_0> A. yellow B. light red C. light orange D. light blue
A
color
[ "A. yellow", "B. light red", "C. light orange", "D. light blue" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=1)", "faces": {"1": [[3.0, 1.0, 1.0000000000000002], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [3.0, 2.0, 1.0000000000000002]], "2": [[2.0, 1.0, 1.0], [2.0, 1.0, 0.0], [2.0, 2.0, 0.0], [2.0, 2.0, 1.0]], "3": [[2, 1, 0], [3, 1, 0], [3, 2, 0], [2, 2, 0]], "4": [[3.0, 1.0, 0.0], [3.0, 1.0, 1.0], [3.0, 2.0, 1.0], [3.0, 2.0, 0.0]], "5": [[3.0, 1.0, 1.0], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [3.0, 2.0, 1.0]], "6": [[3.0, 0.9999999999999999, 1.0], [3.0, 0.9999999999999999, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3", "6"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4"], "6": ["2"]}, "valid": false}, "base_face": "3", "folding_steps": [["4", "3", [3, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "4", [3.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["2", "3", [2, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "2", [2.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["1", "2", [2.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 5 downwards", "Fold face 2 upwards towards face 5", "Fold face 6 inwards towards face 3", "Fold face 1 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net14_base3_step1.png", "output_dir/folding_nets/net14_base3_step2.png", "output_dir/folding_nets/net14_base3_step3.png", "output_dir/folding_nets/net14_base3_step4.png"], "id": "net14_base3"}
2d_perception_color_89_3
What color is face 3 in the cube net shown in the image? <image_0> A. light purple B. light blue C. light red D. yellow
C
color
[ "A. light purple", "B. light blue", "C. light red", "D. yellow" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=1)", "faces": {"1": [[3.0, 1.0, 1.0000000000000002], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [3.0, 2.0, 1.0000000000000002]], "2": [[2.0, 1.0, 1.0], [2.0, 1.0, 0.0], [2.0, 2.0, 0.0], [2.0, 2.0, 1.0]], "3": [[2, 1, 0], [3, 1, 0], [3, 2, 0], [2, 2, 0]], "4": [[3.0, 1.0, 0.0], [3.0, 1.0, 1.0], [3.0, 2.0, 1.0], [3.0, 2.0, 0.0]], "5": [[3.0, 1.0, 1.0], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [3.0, 2.0, 1.0]], "6": [[3.0, 0.9999999999999999, 1.0], [3.0, 0.9999999999999999, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3", "6"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4"], "6": ["2"]}, "valid": false}, "base_face": "3", "folding_steps": [["4", "3", [3, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "4", [3.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["2", "3", [2, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "2", [2.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["1", "2", [2.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 5 downwards", "Fold face 2 upwards towards face 5", "Fold face 6 inwards towards face 3", "Fold face 1 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net14_base3_step1.png", "output_dir/folding_nets/net14_base3_step2.png", "output_dir/folding_nets/net14_base3_step3.png", "output_dir/folding_nets/net14_base3_step4.png"], "id": "net14_base3"}
2d_perception_connectivity_89_2_6
In the cube net shown in the image, is face 2 directly connected to face 6, yes or no? <image_0>
B
connectivity
[ "No", "Yes" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=1)", "faces": {"1": [[3.0, 1.0, 1.0000000000000002], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [3.0, 2.0, 1.0000000000000002]], "2": [[2.0, 1.0, 1.0], [2.0, 1.0, 0.0], [2.0, 2.0, 0.0], [2.0, 2.0, 1.0]], "3": [[2, 1, 0], [3, 1, 0], [3, 2, 0], [2, 2, 0]], "4": [[3.0, 1.0, 0.0], [3.0, 1.0, 1.0], [3.0, 2.0, 1.0], [3.0, 2.0, 0.0]], "5": [[3.0, 1.0, 1.0], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [3.0, 2.0, 1.0]], "6": [[3.0, 0.9999999999999999, 1.0], [3.0, 0.9999999999999999, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3", "6"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4"], "6": ["2"]}, "valid": false}, "base_face": "3", "folding_steps": [["4", "3", [3, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "4", [3.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["2", "3", [2, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "2", [2.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["1", "2", [2.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 5 downwards", "Fold face 2 upwards towards face 5", "Fold face 6 inwards towards face 3", "Fold face 1 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net14_base3_step1.png", "output_dir/folding_nets/net14_base3_step2.png", "output_dir/folding_nets/net14_base3_step3.png", "output_dir/folding_nets/net14_base3_step4.png"], "id": "net14_base3"}
2d_perception_connectivity_89_1_3
In the cube net shown in the image, is face 1 directly connected to face 3, yes or no? <image_0>
A
connectivity
[ "No", "Yes" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=1)", "faces": {"1": [[3.0, 1.0, 1.0000000000000002], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [3.0, 2.0, 1.0000000000000002]], "2": [[2.0, 1.0, 1.0], [2.0, 1.0, 0.0], [2.0, 2.0, 0.0], [2.0, 2.0, 1.0]], "3": [[2, 1, 0], [3, 1, 0], [3, 2, 0], [2, 2, 0]], "4": [[3.0, 1.0, 0.0], [3.0, 1.0, 1.0], [3.0, 2.0, 1.0], [3.0, 2.0, 0.0]], "5": [[3.0, 1.0, 1.0], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [3.0, 2.0, 1.0]], "6": [[3.0, 0.9999999999999999, 1.0], [3.0, 0.9999999999999999, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3", "6"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4"], "6": ["2"]}, "valid": false}, "base_face": "3", "folding_steps": [["4", "3", [3, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "4", [3.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["2", "3", [2, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "2", [2.0, 1.0, 1.0], [0.0, 0.0, -1.0], -1.5707963267948966], ["1", "2", [2.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 4 upwards", "Fold face 5 downwards", "Fold face 2 upwards towards face 5", "Fold face 6 inwards towards face 3", "Fold face 1 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net14_base3_step1.png", "output_dir/folding_nets/net14_base3_step2.png", "output_dir/folding_nets/net14_base3_step3.png", "output_dir/folding_nets/net14_base3_step4.png"], "id": "net14_base3"}
2d_perception_color_90_3
What color is face 3 in the cube net shown in the image? <image_0> A. light blue B. yellow C. light green D. light red
D
color
[ "A. light blue", "B. yellow", "C. light green", "D. light red" ]
{"initial_net": {"name": "Big T Net", "faces": {"4": [[0.9999999999999999, -1.0, 6.123233995736766e-17], [1.0, 0.0, 0.0], [1.0, 6.123233995736765e-17, 1.0], [0.9999999999999999, -0.9999999999999999, 1.0]], "6": [[1.0, 0.0, 0.0], [2.0, 0.0, 0.0], [2.0, 6.123233995736766e-17, 1.0], [1.0, 6.123233995736766e-17, 1.0]], "1": [[2.0, 0.0, 0.0], [2.0, -1.0, 6.123233995736766e-17], [2.0, -0.9999999999999999, 1.0], [2.0, 6.123233995736765e-17, 1.0]], "3": [[1, -1, 0], [2, -1, 0], [2, 0, 0], [1, 0, 0]], "2": [[1.0, -1.0, 1.0], [2.0, -1.0, 1.0], [2.0, -1.0, 0.0], [1.0, -1.0, 0.0]], "5": [[1.0, 0.0, 1.0000000000000002], [2.0, 0.0, 1.0000000000000002], [2.0, -1.0, 1.0], [1.0, -1.0, 1.0]]}, "face_connections": {"4": ["6"], "6": ["4", "1", "3"], "1": ["6"], "3": ["6", "2"], "2": ["3", "5"], "5": ["2"]}, "valid": true}, "base_face": "3", "folding_steps": [["6", "3", [2, 0, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["1", "6", [2.0, 0.0, 0.0], [0.0, 6.123233995736766e-17, 1.0], -1.5707963267948966], ["4", "6", [1.0, 0.0, 0.0], [0.0, 6.123233995736766e-17, 1.0], 1.5707963267948966], ["2", "3", [1, -1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["5", "2", [1.0, -1.0, 1.0], [1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 1 inwards towards face 3", "Fold face 4 inwards towards face 3", "Fold face 2 upwards towards face 4", "Fold face 5 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/random2_net3_base3_step1.png", "output_dir/folding_nets/random2_net3_base3_step2.png", "output_dir/folding_nets/random2_net3_base3_step3.png", "output_dir/folding_nets/random2_net3_base3_step4.png", "output_dir/folding_nets/random2_net3_base3_step5.png", "output_dir/folding_nets/random2_net3_base3_step6.png"], "id": "random2_net3_base3"}
2d_perception_color_90_6
What color is face 6 in the cube net shown in the image? <image_0> A. light red B. light green C. yellow D. light purple
B
color
[ "A. light red", "B. light green", "C. yellow", "D. light purple" ]
{"initial_net": {"name": "Big T Net", "faces": {"4": [[0.9999999999999999, -1.0, 6.123233995736766e-17], [1.0, 0.0, 0.0], [1.0, 6.123233995736765e-17, 1.0], [0.9999999999999999, -0.9999999999999999, 1.0]], "6": [[1.0, 0.0, 0.0], [2.0, 0.0, 0.0], [2.0, 6.123233995736766e-17, 1.0], [1.0, 6.123233995736766e-17, 1.0]], "1": [[2.0, 0.0, 0.0], [2.0, -1.0, 6.123233995736766e-17], [2.0, -0.9999999999999999, 1.0], [2.0, 6.123233995736765e-17, 1.0]], "3": [[1, -1, 0], [2, -1, 0], [2, 0, 0], [1, 0, 0]], "2": [[1.0, -1.0, 1.0], [2.0, -1.0, 1.0], [2.0, -1.0, 0.0], [1.0, -1.0, 0.0]], "5": [[1.0, 0.0, 1.0000000000000002], [2.0, 0.0, 1.0000000000000002], [2.0, -1.0, 1.0], [1.0, -1.0, 1.0]]}, "face_connections": {"4": ["6"], "6": ["4", "1", "3"], "1": ["6"], "3": ["6", "2"], "2": ["3", "5"], "5": ["2"]}, "valid": true}, "base_face": "3", "folding_steps": [["6", "3", [2, 0, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["1", "6", [2.0, 0.0, 0.0], [0.0, 6.123233995736766e-17, 1.0], -1.5707963267948966], ["4", "6", [1.0, 0.0, 0.0], [0.0, 6.123233995736766e-17, 1.0], 1.5707963267948966], ["2", "3", [1, -1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["5", "2", [1.0, -1.0, 1.0], [1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 1 inwards towards face 3", "Fold face 4 inwards towards face 3", "Fold face 2 upwards towards face 4", "Fold face 5 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/random2_net3_base3_step1.png", "output_dir/folding_nets/random2_net3_base3_step2.png", "output_dir/folding_nets/random2_net3_base3_step3.png", "output_dir/folding_nets/random2_net3_base3_step4.png", "output_dir/folding_nets/random2_net3_base3_step5.png", "output_dir/folding_nets/random2_net3_base3_step6.png"], "id": "random2_net3_base3"}
2d_perception_connectivity_90_1_5
In the cube net shown in the image, is face 1 directly connected to face 5, yes or no? <image_0>
A
connectivity
[ "No", "Yes" ]
{"initial_net": {"name": "Big T Net", "faces": {"4": [[0.9999999999999999, -1.0, 6.123233995736766e-17], [1.0, 0.0, 0.0], [1.0, 6.123233995736765e-17, 1.0], [0.9999999999999999, -0.9999999999999999, 1.0]], "6": [[1.0, 0.0, 0.0], [2.0, 0.0, 0.0], [2.0, 6.123233995736766e-17, 1.0], [1.0, 6.123233995736766e-17, 1.0]], "1": [[2.0, 0.0, 0.0], [2.0, -1.0, 6.123233995736766e-17], [2.0, -0.9999999999999999, 1.0], [2.0, 6.123233995736765e-17, 1.0]], "3": [[1, -1, 0], [2, -1, 0], [2, 0, 0], [1, 0, 0]], "2": [[1.0, -1.0, 1.0], [2.0, -1.0, 1.0], [2.0, -1.0, 0.0], [1.0, -1.0, 0.0]], "5": [[1.0, 0.0, 1.0000000000000002], [2.0, 0.0, 1.0000000000000002], [2.0, -1.0, 1.0], [1.0, -1.0, 1.0]]}, "face_connections": {"4": ["6"], "6": ["4", "1", "3"], "1": ["6"], "3": ["6", "2"], "2": ["3", "5"], "5": ["2"]}, "valid": true}, "base_face": "3", "folding_steps": [["6", "3", [2, 0, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["1", "6", [2.0, 0.0, 0.0], [0.0, 6.123233995736766e-17, 1.0], -1.5707963267948966], ["4", "6", [1.0, 0.0, 0.0], [0.0, 6.123233995736766e-17, 1.0], 1.5707963267948966], ["2", "3", [1, -1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["5", "2", [1.0, -1.0, 1.0], [1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 1 inwards towards face 3", "Fold face 4 inwards towards face 3", "Fold face 2 upwards towards face 4", "Fold face 5 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/random2_net3_base3_step1.png", "output_dir/folding_nets/random2_net3_base3_step2.png", "output_dir/folding_nets/random2_net3_base3_step3.png", "output_dir/folding_nets/random2_net3_base3_step4.png", "output_dir/folding_nets/random2_net3_base3_step5.png", "output_dir/folding_nets/random2_net3_base3_step6.png"], "id": "random2_net3_base3"}
2d_perception_connectivity_90_3_5
In the cube net shown in the image, is face 3 directly connected to face 5, yes or no? <image_0>
A
connectivity
[ "No", "Yes" ]
{"initial_net": {"name": "Big T Net", "faces": {"4": [[0.9999999999999999, -1.0, 6.123233995736766e-17], [1.0, 0.0, 0.0], [1.0, 6.123233995736765e-17, 1.0], [0.9999999999999999, -0.9999999999999999, 1.0]], "6": [[1.0, 0.0, 0.0], [2.0, 0.0, 0.0], [2.0, 6.123233995736766e-17, 1.0], [1.0, 6.123233995736766e-17, 1.0]], "1": [[2.0, 0.0, 0.0], [2.0, -1.0, 6.123233995736766e-17], [2.0, -0.9999999999999999, 1.0], [2.0, 6.123233995736765e-17, 1.0]], "3": [[1, -1, 0], [2, -1, 0], [2, 0, 0], [1, 0, 0]], "2": [[1.0, -1.0, 1.0], [2.0, -1.0, 1.0], [2.0, -1.0, 0.0], [1.0, -1.0, 0.0]], "5": [[1.0, 0.0, 1.0000000000000002], [2.0, 0.0, 1.0000000000000002], [2.0, -1.0, 1.0], [1.0, -1.0, 1.0]]}, "face_connections": {"4": ["6"], "6": ["4", "1", "3"], "1": ["6"], "3": ["6", "2"], "2": ["3", "5"], "5": ["2"]}, "valid": true}, "base_face": "3", "folding_steps": [["6", "3", [2, 0, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["1", "6", [2.0, 0.0, 0.0], [0.0, 6.123233995736766e-17, 1.0], -1.5707963267948966], ["4", "6", [1.0, 0.0, 0.0], [0.0, 6.123233995736766e-17, 1.0], 1.5707963267948966], ["2", "3", [1, -1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["5", "2", [1.0, -1.0, 1.0], [1.0, 0.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 1 inwards towards face 3", "Fold face 4 inwards towards face 3", "Fold face 2 upwards towards face 4", "Fold face 5 downwards towards face 4"], "images_per_step": ["output_dir/folding_nets/random2_net3_base3_step1.png", "output_dir/folding_nets/random2_net3_base3_step2.png", "output_dir/folding_nets/random2_net3_base3_step3.png", "output_dir/folding_nets/random2_net3_base3_step4.png", "output_dir/folding_nets/random2_net3_base3_step5.png", "output_dir/folding_nets/random2_net3_base3_step6.png"], "id": "random2_net3_base3"}
2d_perception_color_91_1
What color is face 1 in the cube net shown in the image? <image_0> A. light purple B. light green C. yellow D. light blue
C
color
[ "A. light purple", "B. light green", "C. yellow", "D. light blue" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=1)", "faces": {"5": [[0.9999999999999999, 1.0, 1.0], [1.0, 1.0, 0.0], [1.0, 2.0, 0.0], [0.9999999999999999, 2.0, 1.0]], "6": [[1, 1, 0], [2, 1, 0], [2, 2, 0], [1, 2, 0]], "2": [[2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0]], "4": [[2.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, 2.0, 1.0], [2.0, 2.0, 1.0]], "1": [[1.0, 1.0, 1.0], [0.9999999999999997, 1.0, 0.0], [0.9999999999999997, 2.0, 0.0], [1.0, 2.0, 1.0]], "3": [[1.0, 0.9999999999999999, 1.0], [2.0, 0.9999999999999999, 1.0], [2.0, 1.0, 0.0], [1.0, 1.0, 0.0]]}, "face_connections": {"5": ["6"], "6": ["5", "2", "3"], "2": ["6", "4"], "4": ["2", "1"], "1": ["4"], "3": ["6"]}, "valid": false}, "base_face": "6", "folding_steps": [["3", "6", [1, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["5", "6", [1, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "6", [2, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "2", [2.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "4", [1.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 5 upwards towards face 3", "Fold face 2 upwards towards face 3", "Fold face 4 downwards towards face 5", "Fold face 1 downwards towards face 5"], "images_per_step": ["output_dir/folding_nets/random2_net14_base6_step1.png", "output_dir/folding_nets/random2_net14_base6_step2.png", "output_dir/folding_nets/random2_net14_base6_step3.png", "output_dir/folding_nets/random2_net14_base6_step4.png"], "id": "random2_net14_base6"}
2d_perception_color_91_5
What color is face 5 in the cube net shown in the image? <image_0> A. light green B. light orange C. light purple D. light blue
B
color
[ "A. light green", "B. light orange", "C. light purple", "D. light blue" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=1)", "faces": {"5": [[0.9999999999999999, 1.0, 1.0], [1.0, 1.0, 0.0], [1.0, 2.0, 0.0], [0.9999999999999999, 2.0, 1.0]], "6": [[1, 1, 0], [2, 1, 0], [2, 2, 0], [1, 2, 0]], "2": [[2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0]], "4": [[2.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, 2.0, 1.0], [2.0, 2.0, 1.0]], "1": [[1.0, 1.0, 1.0], [0.9999999999999997, 1.0, 0.0], [0.9999999999999997, 2.0, 0.0], [1.0, 2.0, 1.0]], "3": [[1.0, 0.9999999999999999, 1.0], [2.0, 0.9999999999999999, 1.0], [2.0, 1.0, 0.0], [1.0, 1.0, 0.0]]}, "face_connections": {"5": ["6"], "6": ["5", "2", "3"], "2": ["6", "4"], "4": ["2", "1"], "1": ["4"], "3": ["6"]}, "valid": false}, "base_face": "6", "folding_steps": [["3", "6", [1, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["5", "6", [1, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "6", [2, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "2", [2.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "4", [1.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 5 upwards towards face 3", "Fold face 2 upwards towards face 3", "Fold face 4 downwards towards face 5", "Fold face 1 downwards towards face 5"], "images_per_step": ["output_dir/folding_nets/random2_net14_base6_step1.png", "output_dir/folding_nets/random2_net14_base6_step2.png", "output_dir/folding_nets/random2_net14_base6_step3.png", "output_dir/folding_nets/random2_net14_base6_step4.png"], "id": "random2_net14_base6"}
2d_perception_connectivity_91_2_4
In the cube net shown in the image, is face 2 directly connected to face 4, yes or no? <image_0>
B
connectivity
[ "No", "Yes" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=1)", "faces": {"5": [[0.9999999999999999, 1.0, 1.0], [1.0, 1.0, 0.0], [1.0, 2.0, 0.0], [0.9999999999999999, 2.0, 1.0]], "6": [[1, 1, 0], [2, 1, 0], [2, 2, 0], [1, 2, 0]], "2": [[2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0]], "4": [[2.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, 2.0, 1.0], [2.0, 2.0, 1.0]], "1": [[1.0, 1.0, 1.0], [0.9999999999999997, 1.0, 0.0], [0.9999999999999997, 2.0, 0.0], [1.0, 2.0, 1.0]], "3": [[1.0, 0.9999999999999999, 1.0], [2.0, 0.9999999999999999, 1.0], [2.0, 1.0, 0.0], [1.0, 1.0, 0.0]]}, "face_connections": {"5": ["6"], "6": ["5", "2", "3"], "2": ["6", "4"], "4": ["2", "1"], "1": ["4"], "3": ["6"]}, "valid": false}, "base_face": "6", "folding_steps": [["3", "6", [1, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["5", "6", [1, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "6", [2, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "2", [2.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "4", [1.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 5 upwards towards face 3", "Fold face 2 upwards towards face 3", "Fold face 4 downwards towards face 5", "Fold face 1 downwards towards face 5"], "images_per_step": ["output_dir/folding_nets/random2_net14_base6_step1.png", "output_dir/folding_nets/random2_net14_base6_step2.png", "output_dir/folding_nets/random2_net14_base6_step3.png", "output_dir/folding_nets/random2_net14_base6_step4.png"], "id": "random2_net14_base6"}
2d_perception_connectivity_91_5_1
In the cube net shown in the image, is face 5 directly connected to face 1, yes or no? <image_0>
B
connectivity
[ "Yes", "No" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=1)", "faces": {"5": [[0.9999999999999999, 1.0, 1.0], [1.0, 1.0, 0.0], [1.0, 2.0, 0.0], [0.9999999999999999, 2.0, 1.0]], "6": [[1, 1, 0], [2, 1, 0], [2, 2, 0], [1, 2, 0]], "2": [[2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0]], "4": [[2.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, 2.0, 1.0], [2.0, 2.0, 1.0]], "1": [[1.0, 1.0, 1.0], [0.9999999999999997, 1.0, 0.0], [0.9999999999999997, 2.0, 0.0], [1.0, 2.0, 1.0]], "3": [[1.0, 0.9999999999999999, 1.0], [2.0, 0.9999999999999999, 1.0], [2.0, 1.0, 0.0], [1.0, 1.0, 0.0]]}, "face_connections": {"5": ["6"], "6": ["5", "2", "3"], "2": ["6", "4"], "4": ["2", "1"], "1": ["4"], "3": ["6"]}, "valid": false}, "base_face": "6", "folding_steps": [["3", "6", [1, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["5", "6", [1, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "6", [2, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "2", [2.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "4", [1.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 5 upwards towards face 3", "Fold face 2 upwards towards face 3", "Fold face 4 downwards towards face 5", "Fold face 1 downwards towards face 5"], "images_per_step": ["output_dir/folding_nets/random2_net14_base6_step1.png", "output_dir/folding_nets/random2_net14_base6_step2.png", "output_dir/folding_nets/random2_net14_base6_step3.png", "output_dir/folding_nets/random2_net14_base6_step4.png"], "id": "random2_net14_base6"}
2d_perception_color_92_5
What color is face 5 in the cube net shown in the image? <image_0> A. yellow B. light orange C. light blue D. light green
B
color
[ "A. yellow", "B. light orange", "C. light blue", "D. light green" ]
{"initial_net": {"name": "2 Rows of 3", "faces": {"6": [[0.0, 1.0, 0.0], [1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [0.0, 1.0, 1.0]], "5": [[1.0, 1.0, 0.0], [1.0, 0.0, 0.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0]], "2": [[2.0, 0.0, 0.9999999999999999], [2.0, -1.0, 0.9999999999999999], [1.0, -1.0, 1.0], [1.0, 0.0, 1.0]], "4": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]], "3": [[1.0, 0.0, 0.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 0.0]], "1": [[2.0, 0.0, -6.123233995736766e-17], [2.0, -1.0, -6.123233995736766e-17], [2.0, -1.0, 0.9999999999999999], [2.0, 0.0, 0.9999999999999999]]}, "face_connections": {"6": ["5", "4"], "5": ["6", "2", "3"], "2": ["5", "1"], "4": ["6", "3"], "3": ["5", "4", "1"], "1": ["2", "3"]}, "valid": false}, "base_face": "4", "folding_steps": [["6", "4", [1, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["5", "6", [1.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["3", "4", [1, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "3", [2.0, 0.0, -6.123233995736766e-17], [0.0, -1.0, 0.0], -1.5707963267948966], ["2", "5", [2.0, 0.0, 0.9999999999999999], [0.0, -1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 5 inwards towards face 4", "Fold face 3 upwards towards face 6", "Fold face 1 upwards", "Fold face 2 downwards"], "images_per_step": ["output_dir/folding_nets/random2_net18_base4_step1.png", "output_dir/folding_nets/random2_net18_base4_step2.png"], "id": "random2_net18_base4"}
2d_perception_color_92_2
What color is face 2 in the cube net shown in the image? <image_0> A. light orange B. light purple C. light red D. light green
B
color
[ "A. light orange", "B. light purple", "C. light red", "D. light green" ]
{"initial_net": {"name": "2 Rows of 3", "faces": {"6": [[0.0, 1.0, 0.0], [1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [0.0, 1.0, 1.0]], "5": [[1.0, 1.0, 0.0], [1.0, 0.0, 0.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0]], "2": [[2.0, 0.0, 0.9999999999999999], [2.0, -1.0, 0.9999999999999999], [1.0, -1.0, 1.0], [1.0, 0.0, 1.0]], "4": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]], "3": [[1.0, 0.0, 0.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 0.0]], "1": [[2.0, 0.0, -6.123233995736766e-17], [2.0, -1.0, -6.123233995736766e-17], [2.0, -1.0, 0.9999999999999999], [2.0, 0.0, 0.9999999999999999]]}, "face_connections": {"6": ["5", "4"], "5": ["6", "2", "3"], "2": ["5", "1"], "4": ["6", "3"], "3": ["5", "4", "1"], "1": ["2", "3"]}, "valid": false}, "base_face": "4", "folding_steps": [["6", "4", [1, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["5", "6", [1.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["3", "4", [1, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "3", [2.0, 0.0, -6.123233995736766e-17], [0.0, -1.0, 0.0], -1.5707963267948966], ["2", "5", [2.0, 0.0, 0.9999999999999999], [0.0, -1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 5 inwards towards face 4", "Fold face 3 upwards towards face 6", "Fold face 1 upwards", "Fold face 2 downwards"], "images_per_step": ["output_dir/folding_nets/random2_net18_base4_step1.png", "output_dir/folding_nets/random2_net18_base4_step2.png"], "id": "random2_net18_base4"}
2d_perception_connectivity_92_2_4
In the cube net shown in the image, is face 2 directly connected to face 4, yes or no? <image_0>
B
connectivity
[ "Yes", "No" ]
{"initial_net": {"name": "2 Rows of 3", "faces": {"6": [[0.0, 1.0, 0.0], [1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [0.0, 1.0, 1.0]], "5": [[1.0, 1.0, 0.0], [1.0, 0.0, 0.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0]], "2": [[2.0, 0.0, 0.9999999999999999], [2.0, -1.0, 0.9999999999999999], [1.0, -1.0, 1.0], [1.0, 0.0, 1.0]], "4": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]], "3": [[1.0, 0.0, 0.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 0.0]], "1": [[2.0, 0.0, -6.123233995736766e-17], [2.0, -1.0, -6.123233995736766e-17], [2.0, -1.0, 0.9999999999999999], [2.0, 0.0, 0.9999999999999999]]}, "face_connections": {"6": ["5", "4"], "5": ["6", "2", "3"], "2": ["5", "1"], "4": ["6", "3"], "3": ["5", "4", "1"], "1": ["2", "3"]}, "valid": false}, "base_face": "4", "folding_steps": [["6", "4", [1, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["5", "6", [1.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["3", "4", [1, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "3", [2.0, 0.0, -6.123233995736766e-17], [0.0, -1.0, 0.0], -1.5707963267948966], ["2", "5", [2.0, 0.0, 0.9999999999999999], [0.0, -1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 5 inwards towards face 4", "Fold face 3 upwards towards face 6", "Fold face 1 upwards", "Fold face 2 downwards"], "images_per_step": ["output_dir/folding_nets/random2_net18_base4_step1.png", "output_dir/folding_nets/random2_net18_base4_step2.png"], "id": "random2_net18_base4"}
2d_perception_connectivity_92_6_3
In the cube net shown in the image, is face 6 directly connected to face 3, yes or no? <image_0>
B
connectivity
[ "Yes", "No" ]
{"initial_net": {"name": "2 Rows of 3", "faces": {"6": [[0.0, 1.0, 0.0], [1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [0.0, 1.0, 1.0]], "5": [[1.0, 1.0, 0.0], [1.0, 0.0, 0.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0]], "2": [[2.0, 0.0, 0.9999999999999999], [2.0, -1.0, 0.9999999999999999], [1.0, -1.0, 1.0], [1.0, 0.0, 1.0]], "4": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]], "3": [[1.0, 0.0, 0.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 0.0]], "1": [[2.0, 0.0, -6.123233995736766e-17], [2.0, -1.0, -6.123233995736766e-17], [2.0, -1.0, 0.9999999999999999], [2.0, 0.0, 0.9999999999999999]]}, "face_connections": {"6": ["5", "4"], "5": ["6", "2", "3"], "2": ["5", "1"], "4": ["6", "3"], "3": ["5", "4", "1"], "1": ["2", "3"]}, "valid": false}, "base_face": "4", "folding_steps": [["6", "4", [1, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["5", "6", [1.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["3", "4", [1, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["1", "3", [2.0, 0.0, -6.123233995736766e-17], [0.0, -1.0, 0.0], -1.5707963267948966], ["2", "5", [2.0, 0.0, 0.9999999999999999], [0.0, -1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 5 inwards towards face 4", "Fold face 3 upwards towards face 6", "Fold face 1 upwards", "Fold face 2 downwards"], "images_per_step": ["output_dir/folding_nets/random2_net18_base4_step1.png", "output_dir/folding_nets/random2_net18_base4_step2.png"], "id": "random2_net18_base4"}
2d_perception_color_93_2
What color is face 2 in the cube net shown in the image? <image_0> A. light purple B. light blue C. light green D. light red
A
color
[ "A. light purple", "B. light blue", "C. light green", "D. light red" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=4)", "faces": {"1": [[4.0, 1.0, -9.494107596574928e-16], [5.0, 1.0, 0.0], [5.0, 2.0, 0.0], [4.0, 2.0, -9.494107596574928e-16]], "2": [[5.0, 1.0, 0.0], [5.0, 1.0, 1.0], [5.0, 2.0, 1.0], [5.0, 2.0, 0.0]], "3": [[5.0, 1.0, 1.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [5.0, 2.0, 1.0]], "4": [[4.0, 1.0, 1.0], [4.0, 1.0, 0.0], [4.0, 2.0, 0.0], [4.0, 2.0, 1.0]], "5": [[4, 1, 0], [5, 1, 0], [5, 2, 0], [4, 2, 0]], "6": [[4.0, 0.9999999999999999, 1.0], [5.0, 0.9999999999999999, 1.0], [5.0, 1.0, 0.0], [4.0, 1.0, 0.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": false}, "base_face": "5", "folding_steps": [["6", "5", [4, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["4", "5", [4, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "4", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "3", [5.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["1", "2", [5.0, 1.0, 0.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 4 upwards towards face 6", "Fold face 3 downwards towards face 6", "Fold face 2 downwards towards face 5", "Fold face 1 upwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net17_base5_step1.png", "output_dir/folding_nets/net17_base5_step2.png", "output_dir/folding_nets/net17_base5_step3.png", "output_dir/folding_nets/net17_base5_step4.png"], "id": "net17_base5"}
2d_perception_color_93_6
What color is face 6 in the cube net shown in the image? <image_0> A. yellow B. light blue C. light green D. light red
C
color
[ "A. yellow", "B. light blue", "C. light green", "D. light red" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=4)", "faces": {"1": [[4.0, 1.0, -9.494107596574928e-16], [5.0, 1.0, 0.0], [5.0, 2.0, 0.0], [4.0, 2.0, -9.494107596574928e-16]], "2": [[5.0, 1.0, 0.0], [5.0, 1.0, 1.0], [5.0, 2.0, 1.0], [5.0, 2.0, 0.0]], "3": [[5.0, 1.0, 1.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [5.0, 2.0, 1.0]], "4": [[4.0, 1.0, 1.0], [4.0, 1.0, 0.0], [4.0, 2.0, 0.0], [4.0, 2.0, 1.0]], "5": [[4, 1, 0], [5, 1, 0], [5, 2, 0], [4, 2, 0]], "6": [[4.0, 0.9999999999999999, 1.0], [5.0, 0.9999999999999999, 1.0], [5.0, 1.0, 0.0], [4.0, 1.0, 0.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": false}, "base_face": "5", "folding_steps": [["6", "5", [4, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["4", "5", [4, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "4", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "3", [5.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["1", "2", [5.0, 1.0, 0.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 4 upwards towards face 6", "Fold face 3 downwards towards face 6", "Fold face 2 downwards towards face 5", "Fold face 1 upwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net17_base5_step1.png", "output_dir/folding_nets/net17_base5_step2.png", "output_dir/folding_nets/net17_base5_step3.png", "output_dir/folding_nets/net17_base5_step4.png"], "id": "net17_base5"}
2d_perception_connectivity_93_2_4
In the cube net shown in the image, is face 2 directly connected to face 4, yes or no? <image_0>
B
connectivity
[ "Yes", "No" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=4)", "faces": {"1": [[4.0, 1.0, -9.494107596574928e-16], [5.0, 1.0, 0.0], [5.0, 2.0, 0.0], [4.0, 2.0, -9.494107596574928e-16]], "2": [[5.0, 1.0, 0.0], [5.0, 1.0, 1.0], [5.0, 2.0, 1.0], [5.0, 2.0, 0.0]], "3": [[5.0, 1.0, 1.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [5.0, 2.0, 1.0]], "4": [[4.0, 1.0, 1.0], [4.0, 1.0, 0.0], [4.0, 2.0, 0.0], [4.0, 2.0, 1.0]], "5": [[4, 1, 0], [5, 1, 0], [5, 2, 0], [4, 2, 0]], "6": [[4.0, 0.9999999999999999, 1.0], [5.0, 0.9999999999999999, 1.0], [5.0, 1.0, 0.0], [4.0, 1.0, 0.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": false}, "base_face": "5", "folding_steps": [["6", "5", [4, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["4", "5", [4, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "4", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "3", [5.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["1", "2", [5.0, 1.0, 0.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 4 upwards towards face 6", "Fold face 3 downwards towards face 6", "Fold face 2 downwards towards face 5", "Fold face 1 upwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net17_base5_step1.png", "output_dir/folding_nets/net17_base5_step2.png", "output_dir/folding_nets/net17_base5_step3.png", "output_dir/folding_nets/net17_base5_step4.png"], "id": "net17_base5"}
2d_perception_connectivity_93_1_6
In the cube net shown in the image, is face 1 directly connected to face 6, yes or no? <image_0>
B
connectivity
[ "Yes", "No" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=4)", "faces": {"1": [[4.0, 1.0, -9.494107596574928e-16], [5.0, 1.0, 0.0], [5.0, 2.0, 0.0], [4.0, 2.0, -9.494107596574928e-16]], "2": [[5.0, 1.0, 0.0], [5.0, 1.0, 1.0], [5.0, 2.0, 1.0], [5.0, 2.0, 0.0]], "3": [[5.0, 1.0, 1.0], [4.0, 1.0, 1.0], [4.0, 2.0, 1.0], [5.0, 2.0, 1.0]], "4": [[4.0, 1.0, 1.0], [4.0, 1.0, 0.0], [4.0, 2.0, 0.0], [4.0, 2.0, 1.0]], "5": [[4, 1, 0], [5, 1, 0], [5, 2, 0], [4, 2, 0]], "6": [[4.0, 0.9999999999999999, 1.0], [5.0, 0.9999999999999999, 1.0], [5.0, 1.0, 0.0], [4.0, 1.0, 0.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": false}, "base_face": "5", "folding_steps": [["6", "5", [4, 1, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["4", "5", [4, 1, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["3", "4", [4.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["2", "3", [5.0, 1.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966], ["1", "2", [5.0, 1.0, 0.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 4 upwards towards face 6", "Fold face 3 downwards towards face 6", "Fold face 2 downwards towards face 5", "Fold face 1 upwards towards face 4"], "images_per_step": ["output_dir/folding_nets/net17_base5_step1.png", "output_dir/folding_nets/net17_base5_step2.png", "output_dir/folding_nets/net17_base5_step3.png", "output_dir/folding_nets/net17_base5_step4.png"], "id": "net17_base5"}
2d_perception_color_94_6
What color is face 6 in the cube net shown in the image? <image_0> A. light green B. light red C. light purple D. light orange
A
color
[ "A. light green", "B. light red", "C. light purple", "D. light orange" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=3)", "faces": {"1": [[0, 1, 0], [1, 1, 0], [1, 2, 0], [0, 2, 0]], "2": [[1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0]], "3": [[1.0, 1.0, 1.0], [0.0, 1.0, 1.0000000000000002], [0.0, 2.0, 1.0000000000000002], [1.0, 2.0, 1.0]], "4": [[0.0, 1.0, 1.0000000000000002], [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [-2.83276944882399e-16, 2.0, 2.220446049250313e-16], [0.0, 2.0, 1.0000000000000002]], "5": [[-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.9999999999999997, 1.0, 9.957992501029596e-17], [0.9999999999999997, 2.0, 9.957992501029596e-17], [-2.83276944882399e-16, 2.0, 2.220446049250313e-16]], "6": [[1.0, 0.9999999999999999, 0.9999999999999999], [0.9999999999999997, 0.9999999999999999, 0.0], [-2.8327694488239893e-16, 1.0, 2.220446049250313e-16], [0.0, 1.0, 1.0000000000000002]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5", "6"], "5": ["4"], "6": ["4"]}, "valid": false}, "base_face": "1", "folding_steps": [["2", "1", [1, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "2", [1.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "3", [0.0, 1.0, 1.0000000000000002], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "4", [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "4", [0.0, 1.0, 1.0000000000000002], [-2.83276944882399e-16, 0.0, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 3 downwards", "Fold face 4 downwards towards face 1", "Fold face 5 upwards towards face 1", "Fold face 6 downwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net16_base1_step1.png", "output_dir/folding_nets/net16_base1_step2.png", "output_dir/folding_nets/net16_base1_step3.png"], "id": "net16_base1"}
2d_perception_color_94_1
What color is face 1 in the cube net shown in the image? <image_0> A. light red B. light green C. light purple D. yellow
D
color
[ "A. light red", "B. light green", "C. light purple", "D. yellow" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=3)", "faces": {"1": [[0, 1, 0], [1, 1, 0], [1, 2, 0], [0, 2, 0]], "2": [[1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0]], "3": [[1.0, 1.0, 1.0], [0.0, 1.0, 1.0000000000000002], [0.0, 2.0, 1.0000000000000002], [1.0, 2.0, 1.0]], "4": [[0.0, 1.0, 1.0000000000000002], [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [-2.83276944882399e-16, 2.0, 2.220446049250313e-16], [0.0, 2.0, 1.0000000000000002]], "5": [[-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.9999999999999997, 1.0, 9.957992501029596e-17], [0.9999999999999997, 2.0, 9.957992501029596e-17], [-2.83276944882399e-16, 2.0, 2.220446049250313e-16]], "6": [[1.0, 0.9999999999999999, 0.9999999999999999], [0.9999999999999997, 0.9999999999999999, 0.0], [-2.8327694488239893e-16, 1.0, 2.220446049250313e-16], [0.0, 1.0, 1.0000000000000002]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5", "6"], "5": ["4"], "6": ["4"]}, "valid": false}, "base_face": "1", "folding_steps": [["2", "1", [1, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "2", [1.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "3", [0.0, 1.0, 1.0000000000000002], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "4", [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "4", [0.0, 1.0, 1.0000000000000002], [-2.83276944882399e-16, 0.0, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 3 downwards", "Fold face 4 downwards towards face 1", "Fold face 5 upwards towards face 1", "Fold face 6 downwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net16_base1_step1.png", "output_dir/folding_nets/net16_base1_step2.png", "output_dir/folding_nets/net16_base1_step3.png"], "id": "net16_base1"}
2d_perception_connectivity_94_4_6
In the cube net shown in the image, is face 4 directly connected to face 6, yes or no? <image_0>
B
connectivity
[ "No", "Yes" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=3)", "faces": {"1": [[0, 1, 0], [1, 1, 0], [1, 2, 0], [0, 2, 0]], "2": [[1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0]], "3": [[1.0, 1.0, 1.0], [0.0, 1.0, 1.0000000000000002], [0.0, 2.0, 1.0000000000000002], [1.0, 2.0, 1.0]], "4": [[0.0, 1.0, 1.0000000000000002], [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [-2.83276944882399e-16, 2.0, 2.220446049250313e-16], [0.0, 2.0, 1.0000000000000002]], "5": [[-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.9999999999999997, 1.0, 9.957992501029596e-17], [0.9999999999999997, 2.0, 9.957992501029596e-17], [-2.83276944882399e-16, 2.0, 2.220446049250313e-16]], "6": [[1.0, 0.9999999999999999, 0.9999999999999999], [0.9999999999999997, 0.9999999999999999, 0.0], [-2.8327694488239893e-16, 1.0, 2.220446049250313e-16], [0.0, 1.0, 1.0000000000000002]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5", "6"], "5": ["4"], "6": ["4"]}, "valid": false}, "base_face": "1", "folding_steps": [["2", "1", [1, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "2", [1.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "3", [0.0, 1.0, 1.0000000000000002], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "4", [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "4", [0.0, 1.0, 1.0000000000000002], [-2.83276944882399e-16, 0.0, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 3 downwards", "Fold face 4 downwards towards face 1", "Fold face 5 upwards towards face 1", "Fold face 6 downwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net16_base1_step1.png", "output_dir/folding_nets/net16_base1_step2.png", "output_dir/folding_nets/net16_base1_step3.png"], "id": "net16_base1"}
2d_perception_connectivity_94_2_6
In the cube net shown in the image, is face 2 directly connected to face 6, yes or no? <image_0>
A
connectivity
[ "No", "Yes" ]
{"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=3)", "faces": {"1": [[0, 1, 0], [1, 1, 0], [1, 2, 0], [0, 2, 0]], "2": [[1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0]], "3": [[1.0, 1.0, 1.0], [0.0, 1.0, 1.0000000000000002], [0.0, 2.0, 1.0000000000000002], [1.0, 2.0, 1.0]], "4": [[0.0, 1.0, 1.0000000000000002], [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [-2.83276944882399e-16, 2.0, 2.220446049250313e-16], [0.0, 2.0, 1.0000000000000002]], "5": [[-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.9999999999999997, 1.0, 9.957992501029596e-17], [0.9999999999999997, 2.0, 9.957992501029596e-17], [-2.83276944882399e-16, 2.0, 2.220446049250313e-16]], "6": [[1.0, 0.9999999999999999, 0.9999999999999999], [0.9999999999999997, 0.9999999999999999, 0.0], [-2.8327694488239893e-16, 1.0, 2.220446049250313e-16], [0.0, 1.0, 1.0000000000000002]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5", "6"], "5": ["4"], "6": ["4"]}, "valid": false}, "base_face": "1", "folding_steps": [["2", "1", [1, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "2", [1.0, 1.0, 1.0], [0.0, 1.0, 0.0], -1.5707963267948966], ["4", "3", [0.0, 1.0, 1.0000000000000002], [0.0, 1.0, 0.0], -1.5707963267948966], ["5", "4", [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "4", [0.0, 1.0, 1.0000000000000002], [-2.83276944882399e-16, 0.0, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 3 downwards", "Fold face 4 downwards towards face 1", "Fold face 5 upwards towards face 1", "Fold face 6 downwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net16_base1_step1.png", "output_dir/folding_nets/net16_base1_step2.png", "output_dir/folding_nets/net16_base1_step3.png"], "id": "net16_base1"}
2d_perception_color_95_6
What color is face 6 in the cube net shown in the image? <image_0> A. light red B. light orange C. light green D. light purple
C
color
[ "A. light red", "B. light orange", "C. light green", "D. light purple" ]
{"initial_net": {"name": "t-shaped Net Variant 1", "faces": {"3": [[0.9999999999999999, 0.0, 1.0], [1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, 1.0]], "2": [[2.0, 0.0, 1.0], [0.9999999999999999, 0.0, 1.0], [0.9999999999999999, 1.0, 1.0], [2.0, 1.0, 1.0]], "4": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "5": [[2.0, 0.0, 0.0], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]], "6": [[2.0, -6.123233995736766e-17, 1.0], [2.0, -6.123233995736766e-17, 1.1102230246251565e-16], [1.0, 0.0, 0.0], [0.9999999999999999, 0.0, 1.0]], "1": [[1.0, 1.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [1.0, 1.0, 1.0]]}, "face_connections": {"1": ["4"], "2": ["3"], "3": ["2", "4", "6"], "4": ["1", "3", "5"], "5": ["4"], "6": ["3"]}, "valid": true}, "base_face": "4", "folding_steps": [["1", "4", [2, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["5", "4", [2, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "4", [1, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "3", [0.9999999999999999, 0.0, 1.0], [1.1102230246251565e-16, 0.0, -1.0], -1.5707963267948966], ["2", "3", [0.9999999999999999, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 5 upwards towards face 1", "Fold face 3 upwards towards face 1", "Fold face 6 inwards towards face 4", "Fold face 2 downwards towards face 5"], "images_per_step": ["output_dir/folding_nets/net1_base4_step1.png", "output_dir/folding_nets/net1_base4_step2.png", "output_dir/folding_nets/net1_base4_step3.png", "output_dir/folding_nets/net1_base4_step4.png", "output_dir/folding_nets/net1_base4_step5.png", "output_dir/folding_nets/net1_base4_step6.png"], "id": "net1_base4"}
2d_perception_color_95_1
What color is face 1 in the cube net shown in the image? <image_0> A. yellow B. light red C. light orange D. light green
A
color
[ "A. yellow", "B. light red", "C. light orange", "D. light green" ]
{"initial_net": {"name": "t-shaped Net Variant 1", "faces": {"3": [[0.9999999999999999, 0.0, 1.0], [1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, 1.0]], "2": [[2.0, 0.0, 1.0], [0.9999999999999999, 0.0, 1.0], [0.9999999999999999, 1.0, 1.0], [2.0, 1.0, 1.0]], "4": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "5": [[2.0, 0.0, 0.0], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]], "6": [[2.0, -6.123233995736766e-17, 1.0], [2.0, -6.123233995736766e-17, 1.1102230246251565e-16], [1.0, 0.0, 0.0], [0.9999999999999999, 0.0, 1.0]], "1": [[1.0, 1.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [1.0, 1.0, 1.0]]}, "face_connections": {"1": ["4"], "2": ["3"], "3": ["2", "4", "6"], "4": ["1", "3", "5"], "5": ["4"], "6": ["3"]}, "valid": true}, "base_face": "4", "folding_steps": [["1", "4", [2, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["5", "4", [2, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "4", [1, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "3", [0.9999999999999999, 0.0, 1.0], [1.1102230246251565e-16, 0.0, -1.0], -1.5707963267948966], ["2", "3", [0.9999999999999999, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 5 upwards towards face 1", "Fold face 3 upwards towards face 1", "Fold face 6 inwards towards face 4", "Fold face 2 downwards towards face 5"], "images_per_step": ["output_dir/folding_nets/net1_base4_step1.png", "output_dir/folding_nets/net1_base4_step2.png", "output_dir/folding_nets/net1_base4_step3.png", "output_dir/folding_nets/net1_base4_step4.png", "output_dir/folding_nets/net1_base4_step5.png", "output_dir/folding_nets/net1_base4_step6.png"], "id": "net1_base4"}
2d_perception_connectivity_95_5_6
In the cube net shown in the image, is face 5 directly connected to face 6, yes or no? <image_0>
B
connectivity
[ "Yes", "No" ]
{"initial_net": {"name": "t-shaped Net Variant 1", "faces": {"3": [[0.9999999999999999, 0.0, 1.0], [1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, 1.0]], "2": [[2.0, 0.0, 1.0], [0.9999999999999999, 0.0, 1.0], [0.9999999999999999, 1.0, 1.0], [2.0, 1.0, 1.0]], "4": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "5": [[2.0, 0.0, 0.0], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]], "6": [[2.0, -6.123233995736766e-17, 1.0], [2.0, -6.123233995736766e-17, 1.1102230246251565e-16], [1.0, 0.0, 0.0], [0.9999999999999999, 0.0, 1.0]], "1": [[1.0, 1.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [1.0, 1.0, 1.0]]}, "face_connections": {"1": ["4"], "2": ["3"], "3": ["2", "4", "6"], "4": ["1", "3", "5"], "5": ["4"], "6": ["3"]}, "valid": true}, "base_face": "4", "folding_steps": [["1", "4", [2, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["5", "4", [2, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "4", [1, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "3", [0.9999999999999999, 0.0, 1.0], [1.1102230246251565e-16, 0.0, -1.0], -1.5707963267948966], ["2", "3", [0.9999999999999999, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 5 upwards towards face 1", "Fold face 3 upwards towards face 1", "Fold face 6 inwards towards face 4", "Fold face 2 downwards towards face 5"], "images_per_step": ["output_dir/folding_nets/net1_base4_step1.png", "output_dir/folding_nets/net1_base4_step2.png", "output_dir/folding_nets/net1_base4_step3.png", "output_dir/folding_nets/net1_base4_step4.png", "output_dir/folding_nets/net1_base4_step5.png", "output_dir/folding_nets/net1_base4_step6.png"], "id": "net1_base4"}
2d_perception_connectivity_95_4_1
In the cube net shown in the image, is face 4 directly connected to face 1, yes or no? <image_0>
A
connectivity
[ "Yes", "No" ]
{"initial_net": {"name": "t-shaped Net Variant 1", "faces": {"3": [[0.9999999999999999, 0.0, 1.0], [1.0, 0.0, 0.0], [1.0, 1.0, 0.0], [0.9999999999999999, 1.0, 1.0]], "2": [[2.0, 0.0, 1.0], [0.9999999999999999, 0.0, 1.0], [0.9999999999999999, 1.0, 1.0], [2.0, 1.0, 1.0]], "4": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "5": [[2.0, 0.0, 0.0], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]], "6": [[2.0, -6.123233995736766e-17, 1.0], [2.0, -6.123233995736766e-17, 1.1102230246251565e-16], [1.0, 0.0, 0.0], [0.9999999999999999, 0.0, 1.0]], "1": [[1.0, 1.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [1.0, 1.0, 1.0]]}, "face_connections": {"1": ["4"], "2": ["3"], "3": ["2", "4", "6"], "4": ["1", "3", "5"], "5": ["4"], "6": ["3"]}, "valid": true}, "base_face": "4", "folding_steps": [["1", "4", [2, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["5", "4", [2, 0, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["3", "4", [1, 0, 0], [0.0, 1.0, 0.0], 1.5707963267948966], ["6", "3", [0.9999999999999999, 0.0, 1.0], [1.1102230246251565e-16, 0.0, -1.0], -1.5707963267948966], ["2", "3", [0.9999999999999999, 0.0, 1.0], [0.0, 1.0, 0.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 1 upwards", "Fold face 5 upwards towards face 1", "Fold face 3 upwards towards face 1", "Fold face 6 inwards towards face 4", "Fold face 2 downwards towards face 5"], "images_per_step": ["output_dir/folding_nets/net1_base4_step1.png", "output_dir/folding_nets/net1_base4_step2.png", "output_dir/folding_nets/net1_base4_step3.png", "output_dir/folding_nets/net1_base4_step4.png", "output_dir/folding_nets/net1_base4_step5.png", "output_dir/folding_nets/net1_base4_step6.png"], "id": "net1_base4"}
2d_perception_color_96_6
What color is face 6 in the cube net shown in the image? <image_0> A. light blue B. light red C. yellow D. light green
D
color
[ "A. light blue", "B. light red", "C. yellow", "D. light green" ]
{"initial_net": {"name": "2-2 net", "faces": {"6": [[3.0, -2.8327694488239893e-16, 2.220446049250313e-16], [3.0, 0.0, 1.0000000000000002], [3.0, 1.0, 1.0000000000000002], [3.0, 0.9999999999999997, 2.220446049250313e-16]], "4": [[2.0000000000000004, -2.83276944882399e-16, 0.0], [2.0, 0.0, 1.0], [3.0, 0.0, 1.0000000000000002], [3.0, -2.83276944882399e-16, 2.220446049250313e-16]], "5": [[2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [3.0, 1.0, 1.0000000000000002], [3.0, 0.0, 1.0000000000000002]], "2": [[2.0, 0.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [2.0, 0.0, 1.0]], "3": [[2.0, 1.0, 0.0], [3.0, 1.0, 0.0], [3.0, 1.0, 1.0], [2.0, 1.0, 1.0]], "1": [[2, 0, 0], [3, 0, 0], [3, 1, 0], [2, 1, 0]]}, "face_connections": {"6": ["4"], "4": ["6", "5"], "5": ["4", "2"], "2": ["5", "3"], "3": ["2", "1"], "1": ["3"]}, "valid": true}, "base_face": "1", "folding_steps": [["3", "1", [3, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["2", "3", [2.0, 1.0, 0.0], [0.0, 0.0, 1.0], 1.5707963267948966], ["5", "2", [2.0, 1.0, 1.0], [0.0, -1.0, 0.0], -1.5707963267948966], ["4", "5", [2.0, 0.0, 1.0], [1.0, 0.0, 2.220446049250313e-16], 1.5707963267948966], ["6", "4", [3.0, 0.0, 1.0000000000000002], [0.0, -2.83276944882399e-16, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 2 inwards towards face 1", "Fold face 5 downwards towards face 3", "Fold face 4 downwards towards face 2", "Fold face 6 downwards towards face 5"], "images_per_step": ["output_dir/folding_nets/random2_net8_base1_step1.png", "output_dir/folding_nets/random2_net8_base1_step2.png", "output_dir/folding_nets/random2_net8_base1_step3.png", "output_dir/folding_nets/random2_net8_base1_step4.png", "output_dir/folding_nets/random2_net8_base1_step5.png", "output_dir/folding_nets/random2_net8_base1_step6.png"], "id": "random2_net8_base1"}
2d_perception_color_96_1
What color is face 1 in the cube net shown in the image? <image_0> A. light red B. light purple C. yellow D. light green
C
color
[ "A. light red", "B. light purple", "C. yellow", "D. light green" ]
{"initial_net": {"name": "2-2 net", "faces": {"6": [[3.0, -2.8327694488239893e-16, 2.220446049250313e-16], [3.0, 0.0, 1.0000000000000002], [3.0, 1.0, 1.0000000000000002], [3.0, 0.9999999999999997, 2.220446049250313e-16]], "4": [[2.0000000000000004, -2.83276944882399e-16, 0.0], [2.0, 0.0, 1.0], [3.0, 0.0, 1.0000000000000002], [3.0, -2.83276944882399e-16, 2.220446049250313e-16]], "5": [[2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [3.0, 1.0, 1.0000000000000002], [3.0, 0.0, 1.0000000000000002]], "2": [[2.0, 0.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [2.0, 0.0, 1.0]], "3": [[2.0, 1.0, 0.0], [3.0, 1.0, 0.0], [3.0, 1.0, 1.0], [2.0, 1.0, 1.0]], "1": [[2, 0, 0], [3, 0, 0], [3, 1, 0], [2, 1, 0]]}, "face_connections": {"6": ["4"], "4": ["6", "5"], "5": ["4", "2"], "2": ["5", "3"], "3": ["2", "1"], "1": ["3"]}, "valid": true}, "base_face": "1", "folding_steps": [["3", "1", [3, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["2", "3", [2.0, 1.0, 0.0], [0.0, 0.0, 1.0], 1.5707963267948966], ["5", "2", [2.0, 1.0, 1.0], [0.0, -1.0, 0.0], -1.5707963267948966], ["4", "5", [2.0, 0.0, 1.0], [1.0, 0.0, 2.220446049250313e-16], 1.5707963267948966], ["6", "4", [3.0, 0.0, 1.0000000000000002], [0.0, -2.83276944882399e-16, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 2 inwards towards face 1", "Fold face 5 downwards towards face 3", "Fold face 4 downwards towards face 2", "Fold face 6 downwards towards face 5"], "images_per_step": ["output_dir/folding_nets/random2_net8_base1_step1.png", "output_dir/folding_nets/random2_net8_base1_step2.png", "output_dir/folding_nets/random2_net8_base1_step3.png", "output_dir/folding_nets/random2_net8_base1_step4.png", "output_dir/folding_nets/random2_net8_base1_step5.png", "output_dir/folding_nets/random2_net8_base1_step6.png"], "id": "random2_net8_base1"}
2d_perception_connectivity_96_5_2
In the cube net shown in the image, is face 5 directly connected to face 2, yes or no? <image_0>
B
connectivity
[ "No", "Yes" ]
{"initial_net": {"name": "2-2 net", "faces": {"6": [[3.0, -2.8327694488239893e-16, 2.220446049250313e-16], [3.0, 0.0, 1.0000000000000002], [3.0, 1.0, 1.0000000000000002], [3.0, 0.9999999999999997, 2.220446049250313e-16]], "4": [[2.0000000000000004, -2.83276944882399e-16, 0.0], [2.0, 0.0, 1.0], [3.0, 0.0, 1.0000000000000002], [3.0, -2.83276944882399e-16, 2.220446049250313e-16]], "5": [[2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [3.0, 1.0, 1.0000000000000002], [3.0, 0.0, 1.0000000000000002]], "2": [[2.0, 0.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [2.0, 0.0, 1.0]], "3": [[2.0, 1.0, 0.0], [3.0, 1.0, 0.0], [3.0, 1.0, 1.0], [2.0, 1.0, 1.0]], "1": [[2, 0, 0], [3, 0, 0], [3, 1, 0], [2, 1, 0]]}, "face_connections": {"6": ["4"], "4": ["6", "5"], "5": ["4", "2"], "2": ["5", "3"], "3": ["2", "1"], "1": ["3"]}, "valid": true}, "base_face": "1", "folding_steps": [["3", "1", [3, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["2", "3", [2.0, 1.0, 0.0], [0.0, 0.0, 1.0], 1.5707963267948966], ["5", "2", [2.0, 1.0, 1.0], [0.0, -1.0, 0.0], -1.5707963267948966], ["4", "5", [2.0, 0.0, 1.0], [1.0, 0.0, 2.220446049250313e-16], 1.5707963267948966], ["6", "4", [3.0, 0.0, 1.0000000000000002], [0.0, -2.83276944882399e-16, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 2 inwards towards face 1", "Fold face 5 downwards towards face 3", "Fold face 4 downwards towards face 2", "Fold face 6 downwards towards face 5"], "images_per_step": ["output_dir/folding_nets/random2_net8_base1_step1.png", "output_dir/folding_nets/random2_net8_base1_step2.png", "output_dir/folding_nets/random2_net8_base1_step3.png", "output_dir/folding_nets/random2_net8_base1_step4.png", "output_dir/folding_nets/random2_net8_base1_step5.png", "output_dir/folding_nets/random2_net8_base1_step6.png"], "id": "random2_net8_base1"}
2d_perception_connectivity_96_4_1
In the cube net shown in the image, is face 4 directly connected to face 1, yes or no? <image_0>
A
connectivity
[ "No", "Yes" ]
{"initial_net": {"name": "2-2 net", "faces": {"6": [[3.0, -2.8327694488239893e-16, 2.220446049250313e-16], [3.0, 0.0, 1.0000000000000002], [3.0, 1.0, 1.0000000000000002], [3.0, 0.9999999999999997, 2.220446049250313e-16]], "4": [[2.0000000000000004, -2.83276944882399e-16, 0.0], [2.0, 0.0, 1.0], [3.0, 0.0, 1.0000000000000002], [3.0, -2.83276944882399e-16, 2.220446049250313e-16]], "5": [[2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [3.0, 1.0, 1.0000000000000002], [3.0, 0.0, 1.0000000000000002]], "2": [[2.0, 0.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [2.0, 0.0, 1.0]], "3": [[2.0, 1.0, 0.0], [3.0, 1.0, 0.0], [3.0, 1.0, 1.0], [2.0, 1.0, 1.0]], "1": [[2, 0, 0], [3, 0, 0], [3, 1, 0], [2, 1, 0]]}, "face_connections": {"6": ["4"], "4": ["6", "5"], "5": ["4", "2"], "2": ["5", "3"], "3": ["2", "1"], "1": ["3"]}, "valid": true}, "base_face": "1", "folding_steps": [["3", "1", [3, 1, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["2", "3", [2.0, 1.0, 0.0], [0.0, 0.0, 1.0], 1.5707963267948966], ["5", "2", [2.0, 1.0, 1.0], [0.0, -1.0, 0.0], -1.5707963267948966], ["4", "5", [2.0, 0.0, 1.0], [1.0, 0.0, 2.220446049250313e-16], 1.5707963267948966], ["6", "4", [3.0, 0.0, 1.0000000000000002], [0.0, -2.83276944882399e-16, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 2 inwards towards face 1", "Fold face 5 downwards towards face 3", "Fold face 4 downwards towards face 2", "Fold face 6 downwards towards face 5"], "images_per_step": ["output_dir/folding_nets/random2_net8_base1_step1.png", "output_dir/folding_nets/random2_net8_base1_step2.png", "output_dir/folding_nets/random2_net8_base1_step3.png", "output_dir/folding_nets/random2_net8_base1_step4.png", "output_dir/folding_nets/random2_net8_base1_step5.png", "output_dir/folding_nets/random2_net8_base1_step6.png"], "id": "random2_net8_base1"}
2d_perception_color_97_6
What color is face 6 in the cube net shown in the image? <image_0> A. light red B. yellow C. light purple D. light green
D
color
[ "A. light red", "B. yellow", "C. light purple", "D. light green" ]
{"initial_net": {"name": "3-3 Net", "faces": {"1": [[0, 2, 0], [1, 2, 0], [1, 3, 0], [0, 3, 0]], "2": [[0.0, 2.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0], [0.0, 2.0, 0.0]], "3": [[0.0, 3.0, 1.0000000000000002], [1.0, 3.0, 1.0000000000000002], [1.0, 2.0, 1.0], [0.0, 2.0, 1.0]], "4": [[1.0, 3.0, 1.0000000000000002], [1.0, 3.0, 2.220446049250313e-16], [1.0, 2.0, 0.0], [1.0, 2.0, 1.0]], "5": [[0.0, 3.0, 1.0000000000000004], [0.0, 3.0, 4.440892098500626e-16], [1.0, 3.0, 2.220446049250313e-16], [1.0, 3.0, 1.0000000000000002]], "6": [[-6.123233995736766e-17, 2.0, 1.0000000000000007], [-6.123233995736766e-17, 2.0, 6.661338147750939e-16], [0.0, 3.0, 4.440892098500626e-16], [0.0, 3.0, 1.0000000000000004]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "1", "folding_steps": [["2", "1", [0, 2, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["3", "2", [0.0, 2.0, 1.0], [1.0, 0.0, 0.0], -1.5707963267948966], ["4", "3", [1.0, 3.0, 1.0000000000000002], [0.0, -1.0, -2.220446049250313e-16], -1.5707963267948966], ["5", "4", [1.0, 3.0, 1.0000000000000002], [0.0, 0.0, -1.0], -1.5707963267948966], ["6", "5", [0.0, 3.0, 1.0000000000000004], [0.0, 0.0, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 3 downwards", "Fold face 4 downwards towards face 1", "Fold face 5 inwards towards face 1", "Fold face 6 inwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net7_base1_step1.png", "output_dir/folding_nets/net7_base1_step2.png", "output_dir/folding_nets/net7_base1_step3.png", "output_dir/folding_nets/net7_base1_step4.png", "output_dir/folding_nets/net7_base1_step5.png", "output_dir/folding_nets/net7_base1_step6.png"], "id": "net7_base1"}
2d_perception_color_97_3
What color is face 3 in the cube net shown in the image? <image_0> A. yellow B. light red C. light purple D. light blue
B
color
[ "A. yellow", "B. light red", "C. light purple", "D. light blue" ]
{"initial_net": {"name": "3-3 Net", "faces": {"1": [[0, 2, 0], [1, 2, 0], [1, 3, 0], [0, 3, 0]], "2": [[0.0, 2.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0], [0.0, 2.0, 0.0]], "3": [[0.0, 3.0, 1.0000000000000002], [1.0, 3.0, 1.0000000000000002], [1.0, 2.0, 1.0], [0.0, 2.0, 1.0]], "4": [[1.0, 3.0, 1.0000000000000002], [1.0, 3.0, 2.220446049250313e-16], [1.0, 2.0, 0.0], [1.0, 2.0, 1.0]], "5": [[0.0, 3.0, 1.0000000000000004], [0.0, 3.0, 4.440892098500626e-16], [1.0, 3.0, 2.220446049250313e-16], [1.0, 3.0, 1.0000000000000002]], "6": [[-6.123233995736766e-17, 2.0, 1.0000000000000007], [-6.123233995736766e-17, 2.0, 6.661338147750939e-16], [0.0, 3.0, 4.440892098500626e-16], [0.0, 3.0, 1.0000000000000004]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "1", "folding_steps": [["2", "1", [0, 2, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["3", "2", [0.0, 2.0, 1.0], [1.0, 0.0, 0.0], -1.5707963267948966], ["4", "3", [1.0, 3.0, 1.0000000000000002], [0.0, -1.0, -2.220446049250313e-16], -1.5707963267948966], ["5", "4", [1.0, 3.0, 1.0000000000000002], [0.0, 0.0, -1.0], -1.5707963267948966], ["6", "5", [0.0, 3.0, 1.0000000000000004], [0.0, 0.0, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 3 downwards", "Fold face 4 downwards towards face 1", "Fold face 5 inwards towards face 1", "Fold face 6 inwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net7_base1_step1.png", "output_dir/folding_nets/net7_base1_step2.png", "output_dir/folding_nets/net7_base1_step3.png", "output_dir/folding_nets/net7_base1_step4.png", "output_dir/folding_nets/net7_base1_step5.png", "output_dir/folding_nets/net7_base1_step6.png"], "id": "net7_base1"}
2d_perception_connectivity_97_2_3
In the cube net shown in the image, is face 2 directly connected to face 3, yes or no? <image_0>
B
connectivity
[ "No", "Yes" ]
{"initial_net": {"name": "3-3 Net", "faces": {"1": [[0, 2, 0], [1, 2, 0], [1, 3, 0], [0, 3, 0]], "2": [[0.0, 2.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0], [0.0, 2.0, 0.0]], "3": [[0.0, 3.0, 1.0000000000000002], [1.0, 3.0, 1.0000000000000002], [1.0, 2.0, 1.0], [0.0, 2.0, 1.0]], "4": [[1.0, 3.0, 1.0000000000000002], [1.0, 3.0, 2.220446049250313e-16], [1.0, 2.0, 0.0], [1.0, 2.0, 1.0]], "5": [[0.0, 3.0, 1.0000000000000004], [0.0, 3.0, 4.440892098500626e-16], [1.0, 3.0, 2.220446049250313e-16], [1.0, 3.0, 1.0000000000000002]], "6": [[-6.123233995736766e-17, 2.0, 1.0000000000000007], [-6.123233995736766e-17, 2.0, 6.661338147750939e-16], [0.0, 3.0, 4.440892098500626e-16], [0.0, 3.0, 1.0000000000000004]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "1", "folding_steps": [["2", "1", [0, 2, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["3", "2", [0.0, 2.0, 1.0], [1.0, 0.0, 0.0], -1.5707963267948966], ["4", "3", [1.0, 3.0, 1.0000000000000002], [0.0, -1.0, -2.220446049250313e-16], -1.5707963267948966], ["5", "4", [1.0, 3.0, 1.0000000000000002], [0.0, 0.0, -1.0], -1.5707963267948966], ["6", "5", [0.0, 3.0, 1.0000000000000004], [0.0, 0.0, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 3 downwards", "Fold face 4 downwards towards face 1", "Fold face 5 inwards towards face 1", "Fold face 6 inwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net7_base1_step1.png", "output_dir/folding_nets/net7_base1_step2.png", "output_dir/folding_nets/net7_base1_step3.png", "output_dir/folding_nets/net7_base1_step4.png", "output_dir/folding_nets/net7_base1_step5.png", "output_dir/folding_nets/net7_base1_step6.png"], "id": "net7_base1"}
2d_perception_connectivity_97_2_5
In the cube net shown in the image, is face 2 directly connected to face 5, yes or no? <image_0>
A
connectivity
[ "No", "Yes" ]
{"initial_net": {"name": "3-3 Net", "faces": {"1": [[0, 2, 0], [1, 2, 0], [1, 3, 0], [0, 3, 0]], "2": [[0.0, 2.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0], [0.0, 2.0, 0.0]], "3": [[0.0, 3.0, 1.0000000000000002], [1.0, 3.0, 1.0000000000000002], [1.0, 2.0, 1.0], [0.0, 2.0, 1.0]], "4": [[1.0, 3.0, 1.0000000000000002], [1.0, 3.0, 2.220446049250313e-16], [1.0, 2.0, 0.0], [1.0, 2.0, 1.0]], "5": [[0.0, 3.0, 1.0000000000000004], [0.0, 3.0, 4.440892098500626e-16], [1.0, 3.0, 2.220446049250313e-16], [1.0, 3.0, 1.0000000000000002]], "6": [[-6.123233995736766e-17, 2.0, 1.0000000000000007], [-6.123233995736766e-17, 2.0, 6.661338147750939e-16], [0.0, 3.0, 4.440892098500626e-16], [0.0, 3.0, 1.0000000000000004]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "1", "folding_steps": [["2", "1", [0, 2, 0], [1.0, 0.0, 0.0], -1.5707963267948966], ["3", "2", [0.0, 2.0, 1.0], [1.0, 0.0, 0.0], -1.5707963267948966], ["4", "3", [1.0, 3.0, 1.0000000000000002], [0.0, -1.0, -2.220446049250313e-16], -1.5707963267948966], ["5", "4", [1.0, 3.0, 1.0000000000000002], [0.0, 0.0, -1.0], -1.5707963267948966], ["6", "5", [0.0, 3.0, 1.0000000000000004], [0.0, 0.0, -1.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 2 upwards", "Fold face 3 downwards", "Fold face 4 downwards towards face 1", "Fold face 5 inwards towards face 1", "Fold face 6 inwards towards face 1"], "images_per_step": ["output_dir/folding_nets/net7_base1_step1.png", "output_dir/folding_nets/net7_base1_step2.png", "output_dir/folding_nets/net7_base1_step3.png", "output_dir/folding_nets/net7_base1_step4.png", "output_dir/folding_nets/net7_base1_step5.png", "output_dir/folding_nets/net7_base1_step6.png"], "id": "net7_base1"}
2d_perception_color_98_1
What color is face 1 in the cube net shown in the image? <image_0> A. light purple B. yellow C. light blue D. light orange
B
color
[ "A. light purple", "B. yellow", "C. light blue", "D. light orange" ]
{"initial_net": {"name": "2-2 net", "faces": {"1": [[0.9999999999999999, 1.0, 1.0], [1.0, 2.0, 1.0], [2.0, 2.0, 1.0], [2.0, 1.0, 1.0]], "2": [[0.9999999999999999, 1.0, 0.0], [1.0, 2.0, 0.0], [1.0, 2.0, 1.0], [0.9999999999999999, 1.0, 1.0]], "3": [[1.0, 2.0, 0.0], [2.0, 2.0, 0.0], [2.0, 2.0, 1.0], [1.0, 2.0, 1.0]], "4": [[1, 1, 0], [2, 1, 0], [2, 2, 0], [1, 2, 0]], "5": [[2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0]], "6": [[1.0, 0.9999999999999999, 0.0], [1.0, 0.9999999999999999, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "4", "folding_steps": [["3", "4", [2, 2, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["5", "4", [2, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "5", [2.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["2", "3", [1.0, 2.0, 0.0], [0.0, 0.0, 1.0], 1.5707963267948966], ["1", "2", [1.0, 2.0, 1.0], [-1.1102230246251565e-16, -1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 5 upwards towards face 3", "Fold face 6 inwards towards face 4", "Fold face 2 inwards towards face 4", "Fold face 1 downwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net8_base4_step1.png", "output_dir/folding_nets/net8_base4_step2.png", "output_dir/folding_nets/net8_base4_step3.png", "output_dir/folding_nets/net8_base4_step4.png", "output_dir/folding_nets/net8_base4_step5.png", "output_dir/folding_nets/net8_base4_step6.png"], "id": "net8_base4"}
2d_perception_color_98_4
What color is face 4 in the cube net shown in the image? <image_0> A. light blue B. light red C. light green D. light purple
A
color
[ "A. light blue", "B. light red", "C. light green", "D. light purple" ]
{"initial_net": {"name": "2-2 net", "faces": {"1": [[0.9999999999999999, 1.0, 1.0], [1.0, 2.0, 1.0], [2.0, 2.0, 1.0], [2.0, 1.0, 1.0]], "2": [[0.9999999999999999, 1.0, 0.0], [1.0, 2.0, 0.0], [1.0, 2.0, 1.0], [0.9999999999999999, 1.0, 1.0]], "3": [[1.0, 2.0, 0.0], [2.0, 2.0, 0.0], [2.0, 2.0, 1.0], [1.0, 2.0, 1.0]], "4": [[1, 1, 0], [2, 1, 0], [2, 2, 0], [1, 2, 0]], "5": [[2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0]], "6": [[1.0, 0.9999999999999999, 0.0], [1.0, 0.9999999999999999, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "4", "folding_steps": [["3", "4", [2, 2, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["5", "4", [2, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "5", [2.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["2", "3", [1.0, 2.0, 0.0], [0.0, 0.0, 1.0], 1.5707963267948966], ["1", "2", [1.0, 2.0, 1.0], [-1.1102230246251565e-16, -1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 5 upwards towards face 3", "Fold face 6 inwards towards face 4", "Fold face 2 inwards towards face 4", "Fold face 1 downwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net8_base4_step1.png", "output_dir/folding_nets/net8_base4_step2.png", "output_dir/folding_nets/net8_base4_step3.png", "output_dir/folding_nets/net8_base4_step4.png", "output_dir/folding_nets/net8_base4_step5.png", "output_dir/folding_nets/net8_base4_step6.png"], "id": "net8_base4"}
2d_perception_connectivity_98_2_3
In the cube net shown in the image, is face 2 directly connected to face 3, yes or no? <image_0>
B
connectivity
[ "No", "Yes" ]
{"initial_net": {"name": "2-2 net", "faces": {"1": [[0.9999999999999999, 1.0, 1.0], [1.0, 2.0, 1.0], [2.0, 2.0, 1.0], [2.0, 1.0, 1.0]], "2": [[0.9999999999999999, 1.0, 0.0], [1.0, 2.0, 0.0], [1.0, 2.0, 1.0], [0.9999999999999999, 1.0, 1.0]], "3": [[1.0, 2.0, 0.0], [2.0, 2.0, 0.0], [2.0, 2.0, 1.0], [1.0, 2.0, 1.0]], "4": [[1, 1, 0], [2, 1, 0], [2, 2, 0], [1, 2, 0]], "5": [[2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0]], "6": [[1.0, 0.9999999999999999, 0.0], [1.0, 0.9999999999999999, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "4", "folding_steps": [["3", "4", [2, 2, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["5", "4", [2, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "5", [2.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["2", "3", [1.0, 2.0, 0.0], [0.0, 0.0, 1.0], 1.5707963267948966], ["1", "2", [1.0, 2.0, 1.0], [-1.1102230246251565e-16, -1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 5 upwards towards face 3", "Fold face 6 inwards towards face 4", "Fold face 2 inwards towards face 4", "Fold face 1 downwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net8_base4_step1.png", "output_dir/folding_nets/net8_base4_step2.png", "output_dir/folding_nets/net8_base4_step3.png", "output_dir/folding_nets/net8_base4_step4.png", "output_dir/folding_nets/net8_base4_step5.png", "output_dir/folding_nets/net8_base4_step6.png"], "id": "net8_base4"}
2d_perception_connectivity_98_2_5
In the cube net shown in the image, is face 2 directly connected to face 5, yes or no? <image_0>
A
connectivity
[ "No", "Yes" ]
{"initial_net": {"name": "2-2 net", "faces": {"1": [[0.9999999999999999, 1.0, 1.0], [1.0, 2.0, 1.0], [2.0, 2.0, 1.0], [2.0, 1.0, 1.0]], "2": [[0.9999999999999999, 1.0, 0.0], [1.0, 2.0, 0.0], [1.0, 2.0, 1.0], [0.9999999999999999, 1.0, 1.0]], "3": [[1.0, 2.0, 0.0], [2.0, 2.0, 0.0], [2.0, 2.0, 1.0], [1.0, 2.0, 1.0]], "4": [[1, 1, 0], [2, 1, 0], [2, 2, 0], [1, 2, 0]], "5": [[2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [2.0, 2.0, 1.0], [2.0, 2.0, 0.0]], "6": [[1.0, 0.9999999999999999, 0.0], [1.0, 0.9999999999999999, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]]}, "face_connections": {"1": ["2"], "2": ["1", "3"], "3": ["2", "4"], "4": ["3", "5"], "5": ["4", "6"], "6": ["5"]}, "valid": true}, "base_face": "4", "folding_steps": [["3", "4", [2, 2, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["5", "4", [2, 1, 0], [0.0, 1.0, 0.0], -1.5707963267948966], ["6", "5", [2.0, 1.0, 0.0], [0.0, 0.0, 1.0], -1.5707963267948966], ["2", "3", [1.0, 2.0, 0.0], [0.0, 0.0, 1.0], 1.5707963267948966], ["1", "2", [1.0, 2.0, 1.0], [-1.1102230246251565e-16, -1.0, 0.0], -1.5707963267948966]], "folding_step_descs": ["Fold face 3 upwards", "Fold face 5 upwards towards face 3", "Fold face 6 inwards towards face 4", "Fold face 2 inwards towards face 4", "Fold face 1 downwards towards face 3"], "images_per_step": ["output_dir/folding_nets/net8_base4_step1.png", "output_dir/folding_nets/net8_base4_step2.png", "output_dir/folding_nets/net8_base4_step3.png", "output_dir/folding_nets/net8_base4_step4.png", "output_dir/folding_nets/net8_base4_step5.png", "output_dir/folding_nets/net8_base4_step6.png"], "id": "net8_base4"}
2d_perception_color_99_6
What color is face 6 in the cube net shown in the image? <image_0> A. yellow B. light orange C. light green D. light purple
C
color
[ "A. yellow", "B. light orange", "C. light green", "D. light purple" ]
{"initial_net": {"name": "Big T Net", "faces": {"4": [[0.9999999999999999, -2.0, 0.9999999999999998], [1.0, -3.0, 1.0000000000000002], [1.0, -3.0000000000000004, 2.220446049250313e-16], [0.9999999999999999, -2.0000000000000004, -2.220446049250313e-16]], "3": [[1.0, -3.0, 1.0000000000000002], [2.0, -3.0, 1.0000000000000002], [2.0, -3.0000000000000004, 2.220446049250313e-16], [1.0, -3.0000000000000004, 2.220446049250313e-16]], "5": [[2.0, -3.0, 1.0000000000000002], [2.0, -2.0, 0.9999999999999998], [2.0, -2.0000000000000004, -2.220446049250313e-16], [2.0, -3.0000000000000004, 2.220446049250313e-16]], "1": [[1.0, -2.0, 1.0], [2.0, -2.0, 1.0], [2.0, -3.0, 1.0000000000000002], [1.0, -3.0, 1.0000000000000002]], "6": [[1.0, -2.0, 0.0], [2.0, -2.0, 0.0], [2.0, -2.0, 1.0], [1.0, -2.0, 1.0]], "2": [[1, -3, 0], [2, -3, 0], [2, -2, 0], [1, -2, 0]]}, "face_connections": {"4": ["3"], "3": ["4", "5", "1"], "5": ["3"], "1": ["3", "6"], "6": ["1", "2"], "2": ["6"]}, "valid": true}, "base_face": "2", "folding_steps": [["6", "2", [2, -2, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["1", "6", [2.0, -2.0, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["3", "1", [2.0, -3.0, 1.0000000000000002], [-1.0, 0.0, 0.0], -1.5707963267948966], ["5", "3", [2.0, -3.0, 1.0000000000000002], [0.0, -4.440892098500626e-16, -1.0], -1.5707963267948966], ["4", "3", [1.0, -3.0, 1.0000000000000002], [0.0, -4.440892098500626e-16, -1.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 1 downwards", "Fold face 3 downwards towards face 2", "Fold face 5 downwards towards face 1", "Fold face 4 downwards towards face 1"], "images_per_step": ["output_dir/folding_nets/random3_net3_base2_step1.png", "output_dir/folding_nets/random3_net3_base2_step2.png", "output_dir/folding_nets/random3_net3_base2_step3.png", "output_dir/folding_nets/random3_net3_base2_step4.png", "output_dir/folding_nets/random3_net3_base2_step5.png", "output_dir/folding_nets/random3_net3_base2_step6.png"], "id": "random3_net3_base2"}
2d_perception_color_99_5
What color is face 5 in the cube net shown in the image? <image_0> A. yellow B. light purple C. light green D. light orange
D
color
[ "A. yellow", "B. light purple", "C. light green", "D. light orange" ]
{"initial_net": {"name": "Big T Net", "faces": {"4": [[0.9999999999999999, -2.0, 0.9999999999999998], [1.0, -3.0, 1.0000000000000002], [1.0, -3.0000000000000004, 2.220446049250313e-16], [0.9999999999999999, -2.0000000000000004, -2.220446049250313e-16]], "3": [[1.0, -3.0, 1.0000000000000002], [2.0, -3.0, 1.0000000000000002], [2.0, -3.0000000000000004, 2.220446049250313e-16], [1.0, -3.0000000000000004, 2.220446049250313e-16]], "5": [[2.0, -3.0, 1.0000000000000002], [2.0, -2.0, 0.9999999999999998], [2.0, -2.0000000000000004, -2.220446049250313e-16], [2.0, -3.0000000000000004, 2.220446049250313e-16]], "1": [[1.0, -2.0, 1.0], [2.0, -2.0, 1.0], [2.0, -3.0, 1.0000000000000002], [1.0, -3.0, 1.0000000000000002]], "6": [[1.0, -2.0, 0.0], [2.0, -2.0, 0.0], [2.0, -2.0, 1.0], [1.0, -2.0, 1.0]], "2": [[1, -3, 0], [2, -3, 0], [2, -2, 0], [1, -2, 0]]}, "face_connections": {"4": ["3"], "3": ["4", "5", "1"], "5": ["3"], "1": ["3", "6"], "6": ["1", "2"], "2": ["6"]}, "valid": true}, "base_face": "2", "folding_steps": [["6", "2", [2, -2, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["1", "6", [2.0, -2.0, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["3", "1", [2.0, -3.0, 1.0000000000000002], [-1.0, 0.0, 0.0], -1.5707963267948966], ["5", "3", [2.0, -3.0, 1.0000000000000002], [0.0, -4.440892098500626e-16, -1.0], -1.5707963267948966], ["4", "3", [1.0, -3.0, 1.0000000000000002], [0.0, -4.440892098500626e-16, -1.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 1 downwards", "Fold face 3 downwards towards face 2", "Fold face 5 downwards towards face 1", "Fold face 4 downwards towards face 1"], "images_per_step": ["output_dir/folding_nets/random3_net3_base2_step1.png", "output_dir/folding_nets/random3_net3_base2_step2.png", "output_dir/folding_nets/random3_net3_base2_step3.png", "output_dir/folding_nets/random3_net3_base2_step4.png", "output_dir/folding_nets/random3_net3_base2_step5.png", "output_dir/folding_nets/random3_net3_base2_step6.png"], "id": "random3_net3_base2"}
2d_perception_connectivity_99_1_2
In the cube net shown in the image, is face 1 directly connected to face 2, yes or no? <image_0>
A
connectivity
[ "No", "Yes" ]
{"initial_net": {"name": "Big T Net", "faces": {"4": [[0.9999999999999999, -2.0, 0.9999999999999998], [1.0, -3.0, 1.0000000000000002], [1.0, -3.0000000000000004, 2.220446049250313e-16], [0.9999999999999999, -2.0000000000000004, -2.220446049250313e-16]], "3": [[1.0, -3.0, 1.0000000000000002], [2.0, -3.0, 1.0000000000000002], [2.0, -3.0000000000000004, 2.220446049250313e-16], [1.0, -3.0000000000000004, 2.220446049250313e-16]], "5": [[2.0, -3.0, 1.0000000000000002], [2.0, -2.0, 0.9999999999999998], [2.0, -2.0000000000000004, -2.220446049250313e-16], [2.0, -3.0000000000000004, 2.220446049250313e-16]], "1": [[1.0, -2.0, 1.0], [2.0, -2.0, 1.0], [2.0, -3.0, 1.0000000000000002], [1.0, -3.0, 1.0000000000000002]], "6": [[1.0, -2.0, 0.0], [2.0, -2.0, 0.0], [2.0, -2.0, 1.0], [1.0, -2.0, 1.0]], "2": [[1, -3, 0], [2, -3, 0], [2, -2, 0], [1, -2, 0]]}, "face_connections": {"4": ["3"], "3": ["4", "5", "1"], "5": ["3"], "1": ["3", "6"], "6": ["1", "2"], "2": ["6"]}, "valid": true}, "base_face": "2", "folding_steps": [["6", "2", [2, -2, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["1", "6", [2.0, -2.0, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["3", "1", [2.0, -3.0, 1.0000000000000002], [-1.0, 0.0, 0.0], -1.5707963267948966], ["5", "3", [2.0, -3.0, 1.0000000000000002], [0.0, -4.440892098500626e-16, -1.0], -1.5707963267948966], ["4", "3", [1.0, -3.0, 1.0000000000000002], [0.0, -4.440892098500626e-16, -1.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 1 downwards", "Fold face 3 downwards towards face 2", "Fold face 5 downwards towards face 1", "Fold face 4 downwards towards face 1"], "images_per_step": ["output_dir/folding_nets/random3_net3_base2_step1.png", "output_dir/folding_nets/random3_net3_base2_step2.png", "output_dir/folding_nets/random3_net3_base2_step3.png", "output_dir/folding_nets/random3_net3_base2_step4.png", "output_dir/folding_nets/random3_net3_base2_step5.png", "output_dir/folding_nets/random3_net3_base2_step6.png"], "id": "random3_net3_base2"}
2d_perception_connectivity_99_5_6
In the cube net shown in the image, is face 5 directly connected to face 6, yes or no? <image_0>
A
connectivity
[ "No", "Yes" ]
{"initial_net": {"name": "Big T Net", "faces": {"4": [[0.9999999999999999, -2.0, 0.9999999999999998], [1.0, -3.0, 1.0000000000000002], [1.0, -3.0000000000000004, 2.220446049250313e-16], [0.9999999999999999, -2.0000000000000004, -2.220446049250313e-16]], "3": [[1.0, -3.0, 1.0000000000000002], [2.0, -3.0, 1.0000000000000002], [2.0, -3.0000000000000004, 2.220446049250313e-16], [1.0, -3.0000000000000004, 2.220446049250313e-16]], "5": [[2.0, -3.0, 1.0000000000000002], [2.0, -2.0, 0.9999999999999998], [2.0, -2.0000000000000004, -2.220446049250313e-16], [2.0, -3.0000000000000004, 2.220446049250313e-16]], "1": [[1.0, -2.0, 1.0], [2.0, -2.0, 1.0], [2.0, -3.0, 1.0000000000000002], [1.0, -3.0, 1.0000000000000002]], "6": [[1.0, -2.0, 0.0], [2.0, -2.0, 0.0], [2.0, -2.0, 1.0], [1.0, -2.0, 1.0]], "2": [[1, -3, 0], [2, -3, 0], [2, -2, 0], [1, -2, 0]]}, "face_connections": {"4": ["3"], "3": ["4", "5", "1"], "5": ["3"], "1": ["3", "6"], "6": ["1", "2"], "2": ["6"]}, "valid": true}, "base_face": "2", "folding_steps": [["6", "2", [2, -2, 0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["1", "6", [2.0, -2.0, 1.0], [-1.0, 0.0, 0.0], -1.5707963267948966], ["3", "1", [2.0, -3.0, 1.0000000000000002], [-1.0, 0.0, 0.0], -1.5707963267948966], ["5", "3", [2.0, -3.0, 1.0000000000000002], [0.0, -4.440892098500626e-16, -1.0], -1.5707963267948966], ["4", "3", [1.0, -3.0, 1.0000000000000002], [0.0, -4.440892098500626e-16, -1.0], 1.5707963267948966]], "folding_step_descs": ["Fold face 6 upwards", "Fold face 1 downwards", "Fold face 3 downwards towards face 2", "Fold face 5 downwards towards face 1", "Fold face 4 downwards towards face 1"], "images_per_step": ["output_dir/folding_nets/random3_net3_base2_step1.png", "output_dir/folding_nets/random3_net3_base2_step2.png", "output_dir/folding_nets/random3_net3_base2_step3.png", "output_dir/folding_nets/random3_net3_base2_step4.png", "output_dir/folding_nets/random3_net3_base2_step5.png", "output_dir/folding_nets/random3_net3_base2_step6.png"], "id": "random3_net3_base2"}