qid stringlengths 8 32 | question stringlengths 94 436 | images images listlengths 1 6 | answer stringclasses 2
values | question_info stringlengths 1.35k 2.1k | type stringclasses 5
values | choices sequencelengths 2 2 |
|---|---|---|---|---|---|---|
16_q+steps+all_intermediate_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 3 as the base:
Step 1: Fold face 4 upwards
<image_1>
Step 2: Fold face 2 upwards
<image_2>
Step 3: Fold face 5 downwards towards face 2
<image_3>
Step 4: Fold face 6 upwards towards face 2
<image_4>
Based on the above steps, can ... | B | {"initial_net": {"name": "t-shaped Net Variant 1", "faces": {"3": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]], "2": [[-6.123233995736766e-17, 0.0, 1.0], [0.0, 0.0, 0.0], [0.0, 1.0, 0.0], [-6.123233995736766e-17, 1.0, 1.0]], "4": [[1.0, 0.0, 0.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 0.0]], "5": [[1.0, 0.0, 1.0... | q+steps+all_intermediate_vis | [
"no",
"yes"
] | |
98_q+steps+partial_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 4 as the base:
Step 1: Fold face 2 upwards
<image_1>
Step 2: Fold face 5 upwards
<image_2>
Step 3: Fold face 3 inwards towards face 2
<image_3>
Step 4: Fold face 6 downwards towards face 2
<image_4>
Step 5: Fold face 1 inwards to... | B | {"initial_net": {"name": "Big T - Variant 2", "faces": {"1": [[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]], "2": [[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.... | q+steps+partial_vis | [
"no",
"yes"
] | |
100_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "1-3-2 Net", "faces": {"1": [[0.9999999999999999, 1.0, 0.0], [1.0, 2.0, 0.0], [1.0, 2.0, 1.0], [0.9999999999999999, 1.0, 1.0]], "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.... | q_only | [
"yes",
"no"
] | |
140_q+steps+partial_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 1 as the base:
Step 1: Fold face 4 upwards
<image_1>
Step 2: Fold face 3 inwards towards face 1
<image_2>
Step 3: Fold face 2 inwards towards face 1
<image_3>
Step 4: Fold face 5 downwards towards face 2
Step 5: Fold face 6 downw... | B | {"initial_net": {"name": "1-3-2 Net", "faces": {"1": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]], "2": [[0.0, 1.0, 0.0], [0.0, 1.0, 1.0], [-2.83276944882399e-16, 0.0, 1.0], [-2.83276944882399e-16, 0.0, 0.0]], "3": [[1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [0.0, 1.0, 1.0], [0.0, 1.0, 0.0]], "4": [[1.0, 0.0, 0.0], [1.0, 0.0, 1... | q+steps+partial_vis | [
"no",
"yes"
] | |
87_q+steps+partial_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 4 as the base:
Step 1: Fold face 3 upwards
<image_1>
Step 2: Fold face 2 downwards
<image_2>
Step 3: Fold face 5 upwards towards face 1
Step 4: Fold face 6 inwards towards face 2
Step 5: Fold face 1 downwards towards face 4
Based... | A | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=4)", "faces": {"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, 1.0, 1.0], [3.0, 1.0, 1.0], [3.0, 2.0, 1.0], [4.0, 2.0, 1.0]], "3": [[3.0, 1.0, 1.0], [3.0, 1.0, 0.0], [3.0, 2.0, 0.0], [3.0, 2.0, 1.0]], "4": [[3, 1, 0], [4, 1, 0... | q+steps+partial_vis | [
"no",
"yes"
] | |
134_q+steps+partial_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 2 as the base:
Step 1: Fold face 1 upwards
<image_1>
Step 2: Fold face 3 upwards
Step 3: Fold face 4 downwards towards face 1
Step 4: Fold face 5 downwards towards face 1
Step 5: Fold face 6 inwards towards face 1
Based on the ab... | A | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=2)", "faces": {"1": [[0.9999999999999999, 1.0, 1.0], [1.0, 1.0, 0.0], [1.0, 2.0, 0.0], [0.9999999999999999, 2.0, 1.0]], "2": [[1, 1, 0], [2, 1, 0], [2, 2, 0], [1, 2, 0]], "3": [[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.... | q+steps+partial_vis | [
"no",
"yes"
] | |
137_q+steps+all_intermediate_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 2 as the base:
Step 1: Fold face 1 upwards
<image_1>
Step 2: Fold face 3 upwards
<image_2>
Step 4: Fold face 5 downwards towards face 1
Step 5: Fold face 6 downwards towards face 1
Based on the above steps, can the net be folded ... | A | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=4)", "faces": {"1": [[0.9999999999999999, 1.0, 1.0], [1.0, 1.0, 0.0], [1.0, 2.0, 0.0], [0.9999999999999999, 2.0, 1.0]], "2": [[1, 1, 0], [2, 1, 0], [2, 2, 0], [1, 2, 0]], "3": [[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.... | q+steps+all_intermediate_vis | [
"no",
"yes"
] | |
45_q+steps+all_intermediate_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 5 as the base:
Step 1: Fold face 4 upwards
<image_1>
Step 2: Fold face 3 downwards
<image_2>
Step 3: Fold face 2 downwards towards face 5
<image_3>
Step 4: Fold face 6 downwards towards face 2
<image_4>
Based on the above steps, ... | A | {"initial_net": {"name": "t-shaped Net", "faces": {"3": [[3.0, 0.0, 1.0000000000000002], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [3.0, 1.0, 1.0000000000000002]], "1": [[3.0, 1.0, 1.0000000000000002], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0], [3.0, 1.0, 2.220446049250313e-16]], "2": [[3.0000000000000004, 0.0, 2.220446049250313e-16], ... | q+steps+all_intermediate_vis | [
"yes",
"no"
] | |
26_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 4 as the base:
Step 1: Fold face 2 upwards
Step 2: Fold face 3 inwards towards face 4
Step 3: Fold face 5 upwards towards face 3
Step 4: Fold face 6 downwards towards face 2
Step 5: Fold face 1 inwards towards face 4
Based on th... | A | {"initial_net": {"name": "Big T Net", "faces": {"1": [[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]], "2": [[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]], "3"... | q+steps | [
"yes",
"no"
] | |
80_q+steps+all_intermediate_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 2 as the base:
Step 1: Fold face 1 upwards
<image_1>
Step 2: Fold face 4 upwards towards face 1
<image_2>
Step 4: Fold face 5 inwards towards face 2
Step 5: Fold face 6 downwards towards face 1
Based on the above steps, can the n... | B | {"initial_net": {"name": "Net H: Two rows with bottom row shifted right", "faces": {"1": [[0.9999999999999999, 1.0, 1.0], [1.0, 1.0, 0.0], [1.0, 2.0, 0.0], [0.9999999999999999, 2.0, 1.0]], "2": [[1, 1, 0], [2, 1, 0], [2, 2, 0], [1, 2, 0]], "3": [[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": ... | q+steps+all_intermediate_vis | [
"yes",
"no"
] | |
115_q+steps+partial_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 5 as the base:
Step 1: Fold face 4 upwards
<image_1>
Step 2: Fold face 3 downwards
<image_2>
Step 3: Fold face 2 downwards towards face 5
Step 4: Fold face 6 downwards towards face 2
Step 5: Fold face 1 inwards towards face 3
Bas... | B | {"initial_net": {"name": "t-shaped Net Variant 1", "faces": {"3": [[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": [[3.0000000000000004, 0.0, 2.220446049250313e-16], [3.0, 0.0, 1.0000000000000002], [3.0, 1.0, 1.0000000000000002], [3.0000000000000004, 1.0, 2.220446... | q+steps+partial_vis | [
"no",
"yes"
] | |
43_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 2 as the base:
Step 1: Fold face 1 upwards
Step 2: Fold face 3 upwards
Step 3: Fold face 4 inwards towards face 1
Step 4: Fold face 5 downwards towards face 1
Step 5: Fold face 6 downwards towards face 1
Based on the above steps... | A | {"initial_net": {"name": "3-3 Net", "faces": {"1": [[0.0, 2.0, 0.0], [1.0, 2.0, 0.0], [1.0, 2.0, 1.0], [0.0, 2.0, 1.0]], "2": [[0, 1, 0], [1, 1, 0], [1, 2, 0], [0, 2, 0]], "3": [[0.0, 0.9999999999999999, 1.0], [1.0, 0.9999999999999999, 1.0], [1.0, 1.0, 0.0], [0.0, 1.0, 0.0]], "4": [[1.0, 0.9999999999999999, 1.0], [1.0,... | q+steps | [
"yes",
"no"
] | |
35_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 1 as the base:
Step 1: Fold face 5 upwards
Step 2: Fold face 4 inwards towards face 1
Step 3: Fold face 3 inwards towards face 1
Step 4: Fold face 2 inwards towards face 5
Step 5: Fold face 6 downwards towards face 2
Based on th... | B | {"initial_net": {"name": "t-shaped Net Variant 2", "faces": {"3": [[3.0, 2.0000000000000004, 1.0000000000000002], [2.0, 2.0, 1.0], [2.0, 2.0, 1.1102230246251565e-16], [3.0, 2.0000000000000004, 2.220446049250313e-16]], "2": [[3.0, 1.0000000000000004, 1.0000000000000004], [3.0, 2.0000000000000004, 1.0000000000000002], [3... | q+steps | [
"no",
"yes"
] | |
12_q+steps+all_intermediate_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 1 as the base:
Step 1: Fold face 2 upwards
<image_1>
Step 2: Fold face 3 inwards towards face 1
<image_2>
Step 3: Fold face 4 downwards towards face 2
<image_3>
Step 5: Fold face 6 upwards towards face 1
Based on the above steps,... | A | {"initial_net": {"name": "Invalid D", "faces": {"1": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]], "2": [[0.0, 1.0, 0.0], [1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [0.0, 1.0, 1.0]], "3": [[1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [1.0, 0.0, 1.0], [1.0, 0.0, 0.0]], "4": [[1.0, 1.0, 1.0], [1.0, 0.0, 1.0], [0.0, 0.0, 1.0000000000000002],... | q+steps+all_intermediate_vis | [
"no",
"yes"
] | |
111_q+steps+all_intermediate_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 1 as the base:
Step 1: Fold face 3 upwards
<image_1>
Step 2: Fold face 4 inwards towards face 1
<image_2>
Step 3: Fold face 2 inwards towards face 1
<image_3>
Step 4: Fold face 5 downwards towards face 2
<image_4>
Based on the ab... | B | {"initial_net": {"name": "1-3-2 Net", "faces": {"1": [[0, 1, 0], [1, 1, 0], [1, 2, 0], [0, 2, 0]], "2": [[1.0, 2.0, 0.0], [1.0, 2.0, 1.0], [0.0, 2.0, 1.0], [0.0, 2.0, 0.0]], "3": [[1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [1.0, 2.0, 1.0], [1.0, 2.0, 0.0]], "4": [[0.0, 0.9999999999999999, 0.0], [0.0, 0.9999999999999999, 1.0], [... | q+steps+all_intermediate_vis | [
"no",
"yes"
] | |
110_q+steps+all_for_valid_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 6 as the base:
Step 1: Fold face 5 upwards
<image_1>
Step 2: Fold face 4 inwards towards face 6
<image_2>
Step 3: Fold face 3 downwards towards face 5
<image_3>
Step 4: Fold face 2 downwards towards face 5
<image_4>
Step 5: Fold ... | B | {"initial_net": {"name": "1-3-2 Net", "faces": {"1": [[3.0, -1.0000000000000002, 1.1442377452219691e-17], [2.0, -1.0, 6.123233995736766e-17], [2.0, -0.9999999999999999, 1.0], [3.0, -1.0000000000000002, 1.0000000000000002]], "2": [[3.0, -0.9999999999999999, 1.0], [3.0, 1.224646799147353e-16, 1.0], [3.0000000000000004, 1... | q+steps+all_for_valid_vis | [
"no",
"yes"
] | |
57_q+steps+all_for_valid_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 3 as the base:
Step 1: Fold face 2 upwards
<image_1>
Step 2: Fold face 4 inwards towards face 3
<image_2>
Step 3: Fold face 5 inwards towards face 3
<image_3>
Step 4: Fold face 6 inwards towards face 2
<image_4>
Step 5: Fold face... | B | {"initial_net": {"name": "Big T Net", "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, -6.123233995736766e-17, 1.0],... | q+steps+all_for_valid_vis | [
"no",
"yes"
] | |
63_q+steps+all_intermediate_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 1 as the base:
Step 1: Fold face 2 upwards
<image_1>
Step 2: Fold face 4 inwards towards face 1
<image_2>
Step 3: Fold face 5 inwards towards face 1
<image_3>
Step 4: Fold face 6 inwards towards face 1
<image_4>
Based on the abov... | B | {"initial_net": {"name": "Big T - Variant 3", "faces": {"1": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]], "2": [[1.0, 0.0, 0.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 0.0]], "3": [[0.9999999999999999, 1.0, 1.0], [1.0, 0.0, 1.0000000000000002], [0.0, 0.0, 1.0000000000000002], [-1.1102230246251565e-16, 0.99999999... | q+steps+all_intermediate_vis | [
"no",
"yes"
] | |
88_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "t-shaped Net", "faces": {"3": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]], "1": [[0.0, 1.0, 0.0], [1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [0.0, 1.0, 1.0]], "2": [[-6.123233995736766e-17, 0.0, 1.0], [0.0, 0.0, 0.0], [0.0, 1.0, 0.0], [-6.123233995736766e-17, 1.0, 1.0]], "4": [[1.0, 0.0, 0.0], [1.0, 0... | q_only | [
"no",
"yes"
] | |
58_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 3 as the base:
Step 1: Fold face 2 upwards
Step 2: Fold face 4 upwards
Step 3: Fold face 5 downwards towards face 1
Step 4: Fold face 6 downwards towards face 2
Step 5: Fold face 1 downwards towards face 4
Based on the above ste... | A | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=4)", "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.... | q+steps | [
"no",
"yes"
] | |
74_q+steps+all_intermediate_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 5 as the base:
Step 1: Fold face 4 upwards
<image_1>
Step 2: Fold face 3 downwards
<image_2>
Step 3: Fold face 2 downwards towards face 5
<image_3>
Step 5: Fold face 1 upwards towards face 4
Based on the above steps, can the net ... | B | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=2)", "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,... | q+steps+all_intermediate_vis | [
"yes",
"no"
] | |
83_q+steps+all_intermediate_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 6 as the base:
Step 1: Fold face 3 upwards
<image_1>
Step 2: Fold face 5 upwards towards face 3
<image_2>
Step 3: Fold face 4 downwards towards face 3
<image_3>
Step 4: Fold face 2 downwards towards face 3
<image_4>
Based on the ... | A | {"initial_net": {"name": "Big T - Variant 3", "faces": {"1": [[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]], "2": [[1.0, -3.0, 1.0000000000000002], [2.0, -3.0, 1.00000... | q+steps+all_intermediate_vis | [
"yes",
"no"
] | |
95_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 1 as the base:
Step 1: Fold face 3 upwards
Step 2: Fold face 4 inwards towards face 1
Step 3: Fold face 2 inwards towards face 1
Step 4: Fold face 5 inwards towards face 1
Step 5: Fold face 6 downwards towards face 2
Based on th... | B | {"initial_net": {"name": "t-shaped Net", "faces": {"3": [[0.0, 0.9999999999999999, 1.0], [1.0, 0.9999999999999999, 1.0], [1.0, 1.0, 0.0], [0.0, 1.0, 0.0]], "1": [[0, 1, 0], [1, 1, 0], [1, 2, 0], [0, 2, 0]], "2": [[-6.123233995736766e-17, 2.0, 1.0], [0.0, 0.9999999999999999, 1.0], [0.0, 1.0, 0.0], [-6.123233995736766e-1... | q+steps | [
"no",
"yes"
] | |
91_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 5 as the base:
Step 1: Fold face 6 upwards
Step 2: Fold face 4 upwards towards face 6
Step 3: Fold face 3 downwards towards face 6
Step 4: Fold face 2 downwards towards face 5
Step 5: Fold face 1 inwards towards face 3
Based on ... | B | {"initial_net": {"name": "invalid_G", "faces": {"2": [[4.0, 0.0, 0.0], [4.0, 0.0, 1.0], [4.0, 1.0, 1.0], [4.0, 1.0, 0.0]], "3": [[4.0, 0.0, 1.0], [3.0, 0.0, 1.0], [3.0, 1.0, 1.0], [4.0, 1.0, 1.0]], "4": [[3.0, 0.0, 1.0], [3.0, 0.0, 0.0], [3.0, 1.0, 0.0], [3.0, 1.0, 1.0]], "5": [[3, 0, 0], [4, 0, 0], [4, 1, 0], [3, 1, 0... | q+steps | [
"yes",
"no"
] | |
20_q+steps+all_intermediate_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 2 as the base:
Step 1: Fold face 1 upwards
<image_1>
Step 2: Fold face 4 upwards towards face 1
<image_2>
Step 3: Fold face 3 upwards towards face 4
<image_3>
Step 4: Fold face 5 downwards towards face 1
<image_4>
Based on the ab... | A | {"initial_net": {"name": "Big T Net", "faces": {"1": [[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": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "3": [[2.0, 0.0, 0.0], [2.0, 0.0, 1.0], [2.0, 1.0, 1.0], [2.0, 1.0, 0.0]], "4": [[1.0, -6.123233995736766e-17, 1.0],... | q+steps+all_intermediate_vis | [
"yes",
"no"
] | |
60_q+steps+all_intermediate_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 1 as the base:
Step 1: Fold face 2 upwards
<image_1>
Step 3: Fold face 3 inwards
Step 4: Fold face 5 downwards
Step 5: Fold face 6 downwards
Based on the above steps, can the net be folded to form a cube, yes or no? | A | {"initial_net": {"name": "Net H: Two rows with bottom row shifted right", "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], [1.0, 0.9999999999999998, 2.0], [1.0, 1.9999999999999998, 2.0], [1.0, 2.0, 1.0000000000... | q+steps+all_intermediate_vis | [
"no",
"yes"
] | |
11_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 6 as the base:
Step 1: Fold face 3 upwards
Step 2: Fold face 2 inwards towards face 6
Step 3: Fold face 4 inwards towards face 6
Step 4: Fold face 5 inwards towards face 1
Step 5: Fold face 1 inwards towards face 4
Based on the ... | B | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=2)", "faces": {"1": [[3.0, -2.83276944882399e-16, 0.0], [2.0, 0.0, 0.0], [2.0, 0.0, 1.0], [3.0, -2.83276944882399e-16, 1.0]], "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... | q+steps | [
"yes",
"no"
] | |
3_q+steps+all_intermediate_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 3 as the base:
Step 1: Fold face 5 upwards
<image_1>
Step 2: Fold face 4 inwards towards face 3
<image_2>
Step 3: Fold face 2 inwards towards face 3
<image_3>
Step 4: Fold face 6 inwards towards face 2
<image_4>
Based on the abov... | A | {"initial_net": {"name": "Big T - Variant 2", "faces": {"1": [[2.0, -0.9999999999999999, 1.0], [3.0, -0.9999999999999999, 1.0], [3.0, -2.0, 1.0], [2.0, -2.0, 1.0000000000000004]], "2": [[3.0, -0.9999999999999999, 1.0], [3.0, -0.9999999999999999, 0.0], [3.0, -2.0, 0.0], [3.0, -2.0, 1.0]], "3": [[2, -2, 0], [3, -2, 0], [... | q+steps+all_intermediate_vis | [
"yes",
"no"
] | |
118_q+steps+partial_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 4 as the base:
Step 1: Fold face 2 upwards
<image_1>
Step 2: Fold face 5 upwards
<image_2>
Step 3: Fold face 6 downwards towards face 2
Step 4: Fold face 3 downwards towards face 2
Step 5: Fold face 1 inwards towards face 4
Based... | A | {"initial_net": {"name": "Big T - Variant 3", "faces": {"1": [[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]], "2": [[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.... | q+steps+partial_vis | [
"yes",
"no"
] | |
71_q+steps+partial_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 6 as the base:
Step 1: Fold face 5 upwards
<image_1>
Step 2: Fold face 4 inwards towards face 6
<image_2>
Step 3: Fold face 3 downwards towards face 5
Step 4: Fold face 2 downwards towards face 5
Step 5: Fold face 1 downwards tow... | B | {"initial_net": {"name": "1-3-2 Net", "faces": {"1": [[2.0, -1.0000000000000002, 0.0], [2.0, -0.9999999999999999, 1.0], [3.0, -0.9999999999999999, 1.0], [3.0, -1.0000000000000002, 1.1102230246251565e-16]], "2": [[3.0, -0.9999999999999999, 1.0], [3.0, 1.224646799147353e-16, 1.0], [3.0000000000000004, 1.8369701987210294e... | q+steps+partial_vis | [
"no",
"yes"
] | |
67_q+steps+all_intermediate_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 2 as the base:
Step 1: Fold face 1 upwards
<image_1>
Step 2: Fold face 4 upwards towards face 1
<image_2>
Step 3: Fold face 5 downwards towards face 1
<image_3>
Step 4: Fold face 6 downwards towards face 1
<image_4>
Based on the ... | A | {"initial_net": {"name": "Big T - Variant 3", "faces": {"1": [[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": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "3": [[2.0, 1.0, 2.220446049250313e-16], [2.0, 0.0, 1.1102230246251565e-16], [2.0, 0.0, 1.0], [2.0, 0.999999... | q+steps+all_intermediate_vis | [
"yes",
"no"
] | |
23_q+steps+partial_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 6 as the base:
Step 1: Fold face 5 upwards
<image_1>
Step 2: Fold face 4 inwards towards face 6
<image_2>
Step 3: Fold face 3 downwards towards face 5
Step 4: Fold face 2 downwards towards face 5
Step 5: Fold face 1 downwards tow... | B | {"initial_net": {"name": "1-3-2 Net", "faces": {"1": [[2.0, -1.0, 0.9999999999999997], [3.0, -0.9999999999999999, 1.0], [3.0000000000000004, -0.9999999999999998, 0.0], [2.0000000000000004, -0.9999999999999999, -4.440892098500626e-16]], "2": [[3.0, -0.9999999999999999, 1.0], [3.0, 1.224646799147353e-16, 1.0], [3.0000000... | q+steps+partial_vis | [
"no",
"yes"
] | |
47_q+steps+all_intermediate_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 6 as the base:
Step 1: Fold face 3 upwards
<image_1>
Step 2: Fold face 2 inwards towards face 6
<image_2>
Step 3: Fold face 4 inwards towards face 6
<image_3>
Step 4: Fold face 5 downwards towards face 2
<image_4>
Based on the ab... | A | {"initial_net": {"name": "t-shaped Net Variant 2", "faces": {"3": [[0.0, 0.0, 0.0], [1.0, 0.0, 0.0], [1.0, 6.123233995736766e-17, 1.0], [0.0, 6.123233995736766e-17, 1.0]], "2": [[-6.123233995736766e-17, -1.0, 6.123233995736766e-17], [0.0, 0.0, 0.0], [0.0, 6.123233995736765e-17, 1.0], [-6.123233995736766e-17, -0.9999999... | q+steps+all_intermediate_vis | [
"yes",
"no"
] | |
66_q+steps+all_intermediate_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 5 as the base:
Step 1: Fold face 4 upwards
<image_1>
Step 2: Fold face 3 downwards
<image_2>
Step 3: Fold face 2 downwards towards face 5
<image_3>
Step 4: Fold face 6 downwards towards face 2
<image_4>
Based on the above steps, ... | B | {"initial_net": {"name": "t-shaped Net Variant 2", "faces": {"3": [[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": [[3.0000000000000004, 0.0, 2.220446049250313e-16], [3.0, 0.0, 1.0000000000000002], [3.0, 1.0, 1.0000000000000002], [3.0000000000000004, 1.0, 2.220446... | q+steps+all_intermediate_vis | [
"no",
"yes"
] | |
114_q+steps+all_intermediate_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 1 as the base:
Step 1: Fold face 2 upwards
<image_1>
Step 3: Fold face 3 upwards towards face 1
Step 4: Fold face 5 upwards towards face 1
Step 5: Fold face 6 downwards towards face 1
Based on the above steps, can the net be fold... | B | {"initial_net": {"name": "2 Rows of 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, 2.0, 6.123233995736766e-17], [1.0000000000000002, 3.0, 1.2246467991473535e-16], [1.1102230246251565e-16, 3.0, 6.123233995736767e-17]... | q+steps+all_intermediate_vis | [
"yes",
"no"
] | |
49_q+steps+all_intermediate_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 5 as the base:
Step 1: Fold face 6 upwards
<image_1>
Step 2: Fold face 4 upwards
<image_2>
Step 3: Fold face 3 inwards towards face 5
<image_3>
Step 5: Fold face 1 downwards towards face 3
Based on the above steps, can the net be... | B | {"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.... | q+steps+all_intermediate_vis | [
"yes",
"no"
] | |
40_q+steps+all_intermediate_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 3 as the base:
Step 1: Fold face 2 upwards
<image_1>
Step 2: Fold face 4 upwards towards face 2
<image_2>
Step 3: Fold face 5 inwards towards face 3
<image_3>
Step 4: Fold face 6 downwards towards face 2
<image_4>
Based on the ab... | B | {"initial_net": {"name": "2-2 net", "faces": {"1": [[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]], "2": [[0.9999999999999999, 2.0, 1.0], [1.0, 2.0, 0.0], [1.0, 3.0, 0.0], [0.9999999999999999, 3.0, 1.0]], "3": [[1, 2, 0], [2, 2, 0], [2, 3, 0], [1, 3, 0]], "4": [[1.... | q+steps+all_intermediate_vis | [
"no",
"yes"
] | |
13_q+steps+all_for_valid_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 6 as the base:
Step 1: Fold face 5 upwards
<image_1>
Step 2: Fold face 4 downwards
<image_2>
Step 3: Fold face 2 downwards towards face 6
<image_3>
Step 4: Fold face 3 downwards towards face 4
<image_4>
Step 5: Fold face 1 downwa... | A | {"initial_net": {"name": "Big T Net", "faces": {"1": [[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]], "2": [[1.0, -3.0, 1.0000000000000002], [2.0, -3.0, 1.0000000000000... | q+steps+all_for_valid_vis | [
"yes",
"no"
] | |
34_q+steps+all_intermediate_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 5 as the base:
Step 1: Fold face 4 upwards
<image_1>
Step 2: Fold face 3 downwards
<image_2>
Step 3: Fold face 2 downwards towards face 5
<image_3>
Step 5: Fold face 1 upwards towards face 4
Based on the above steps, can the net ... | A | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=3)", "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,... | q+steps+all_intermediate_vis | [
"no",
"yes"
] | |
84_q+steps+all_intermediate_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 2 as the base:
Step 1: Fold face 1 upwards
<image_1>
Step 2: Fold face 4 upwards towards face 1
<image_2>
Step 3: Fold face 5 downwards towards face 1
<image_3>
Step 4: Fold face 3 downwards towards face 2
<image_4>
Based on the ... | A | {"initial_net": {"name": "Big T - Variant 2", "faces": {"1": [[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": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "3": [[2.0, 0.9999999999999999, 1.0000000000000002], [2.0, 1.0, 2.220446049250313e-16], [2.0, 1.110223024625... | q+steps+all_intermediate_vis | [
"yes",
"no"
] | |
15_q+steps+partial_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 2 as the base:
Step 1: Fold face 1 upwards
<image_1>
Step 2: Fold face 3 upwards
Step 3: Fold face 4 downwards towards face 1
Step 4: Fold face 5 downwards towards face 1
Step 5: Fold face 6 downwards towards face 1
Based on the ... | B | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=3)", "faces": {"1": [[0.9999999999999999, 1.0, 1.0], [1.0, 1.0, 0.0], [1.0, 2.0, 0.0], [0.9999999999999999, 2.0, 1.0]], "2": [[1, 1, 0], [2, 1, 0], [2, 2, 0], [1, 2, 0]], "3": [[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.... | q+steps+partial_vis | [
"yes",
"no"
] | |
81_q+steps+partial_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 3 as the base:
Step 1: Fold face 2 upwards
<image_1>
Step 2: Fold face 4 upwards
Step 3: Fold face 5 upwards towards face 2
Step 4: Fold face 6 inwards towards face 2
Step 5: Fold face 1 downwards towards face 4
Based on the abov... | B | {"initial_net": {"name": "invalid_F", "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], [... | q+steps+partial_vis | [
"yes",
"no"
] | |
132_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 4 as the base:
Step 1: Fold face 3 upwards
Step 2: Fold face 2 downwards
Step 3: Fold face 5 inwards towards face 2
Step 4: Fold face 6 upwards towards face 2
Step 5: Fold face 1 downwards towards face 4
Based on the above steps... | B | {"initial_net": {"name": "invalid_F", "faces": {"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, 1.0, 1.0], [3.0, 1.0, 1.0], [3.0, 2.0, 1.0], [4.0, 2.0, 1.0]], "3": [[3.0, 1.0, 1.0], [3.0, 1.0, 0.0], [3.0, 2.0, 0.0], [3.0, 2.0, 1.0]], "4": [[3, 1, 0], [4, 1, 0], [4, 2, 0], [3, 2, 0... | q+steps | [
"yes",
"no"
] | |
126_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 1 as the base:
Step 1: Fold face 2 upwards
Step 2: Fold face 3 downwards
Step 3: Fold face 4 downwards towards face 1
Step 4: Fold face 5 inwards
Step 5: Fold face 6 upwards towards face 3
Based on the above steps, can the net b... | A | {"initial_net": {"name": "invalid_F", "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... | q+steps | [
"no",
"yes"
] | |
115_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 5 as the base:
Step 1: Fold face 4 upwards
Step 2: Fold face 3 downwards
Step 3: Fold face 2 downwards towards face 5
Step 4: Fold face 6 downwards towards face 2
Step 5: Fold face 1 inwards towards face 3
Based on the above ste... | A | {"initial_net": {"name": "t-shaped Net Variant 1", "faces": {"3": [[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": [[3.0000000000000004, 0.0, 2.220446049250313e-16], [3.0, 0.0, 1.0000000000000002], [3.0, 1.0, 1.0000000000000002], [3.0000000000000004, 1.0, 2.220446... | q+steps | [
"yes",
"no"
] | |
92_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 4 as the base:
Step 1: Fold face 3 upwards
Step 2: Fold face 2 inwards towards face 4
Step 3: Fold face 5 upwards towards face 3
Step 4: Fold face 6 inwards towards face 2
Step 5: Fold face 1 downwards towards face 3
Based on th... | B | {"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":... | q+steps | [
"no",
"yes"
] | |
25_q+steps+all_intermediate_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 4 as the base:
Step 1: Fold face 3 upwards
<image_1>
Step 2: Fold face 2 downwards
<image_2>
Step 4: Fold face 6 downwards towards face 1
Step 5: Fold face 1 downwards towards face 4
Based on the above steps, can the net be folde... | B | {"initial_net": {"name": "Linear 6-Face Row", "faces": {"1": [[4.0, 0.0, 0.0], [4.0, 0.0, 1.0], [4.0, 1.0, 1.0], [4.0, 1.0, 0.0]], "2": [[4.0, 0.0, 1.0], [3.0, 0.0, 1.0], [3.0, 1.0, 1.0], [4.0, 1.0, 1.0]], "3": [[3.0, 0.0, 1.0], [3.0, 0.0, 0.0], [3.0, 1.0, 0.0], [3.0, 1.0, 1.0]], "4": [[3, 0, 0], [4, 0, 0], [4, 1, 0], ... | q+steps+all_intermediate_vis | [
"yes",
"no"
] | |
68_q+steps+all_for_valid_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 3 as the base:
Step 1: Fold face 6 upwards
<image_1>
Step 2: Fold face 5 inwards towards face 3
<image_2>
Step 3: Fold face 4 inwards towards face 3
<image_3>
Step 4: Fold face 2 inwards towards face 3
<image_4>
Step 5: Fold face... | B | {"initial_net": {"name": "Big T - Variant 3", "faces": {"1": [[3.0000000000000004, -2.0, 1.0], [3.0000000000000004, -3.0, 1.0], [2.0000000000000004, -3.0, 1.0], [2.0000000000000004, -2.0, 1.0]], "2": [[3.0000000000000004, -3.0, 1.0], [3.0000000000000004, -3.0, 0.0], [2.0000000000000004, -3.0, 0.0], [2.0000000000000004,... | q+steps+all_for_valid_vis | [
"no",
"yes"
] | |
84_q+steps+all_for_valid_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 2 as the base:
Step 1: Fold face 1 upwards
<image_1>
Step 2: Fold face 4 upwards towards face 1
<image_2>
Step 3: Fold face 5 downwards towards face 1
<image_3>
Step 4: Fold face 3 downwards towards face 2
<image_4>
Step 5: Fold ... | A | {"initial_net": {"name": "Big T - Variant 2", "faces": {"1": [[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": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "3": [[2.0, 0.9999999999999999, 1.0000000000000002], [2.0, 1.0, 2.220446049250313e-16], [2.0, 1.110223024625... | q+steps+all_for_valid_vis | [
"yes",
"no"
] | |
31_q+steps+partial_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 2 as the base:
Step 1: Fold face 1 upwards
<image_1>
Step 2: Fold face 3 upwards
Step 3: Fold face 4 downwards towards face 1
Step 4: Fold face 5 downwards
Step 5: Fold face 6 inwards towards face 3
Based on the above steps, can ... | B | {"initial_net": {"name": "invalid_F", "faces": {"1": [[0.9999999999999999, 1.0, 1.0], [1.0, 1.0, 0.0], [1.0, 2.0, 0.0], [0.9999999999999999, 2.0, 1.0]], "2": [[1, 1, 0], [2, 1, 0], [2, 2, 0], [1, 2, 0]], "3": [[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], [... | q+steps+partial_vis | [
"yes",
"no"
] | |
62_q+steps+partial_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 2 as the base:
Step 1: Fold face 1 upwards
<image_1>
Step 2: Fold face 3 upwards
Step 3: Fold face 4 downwards towards face 1
Step 4: Fold face 5 downwards towards face 1
Step 5: Fold face 6 inwards towards face 2
Based on the ab... | B | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=0)", "faces": {"1": [[0.9999999999999999, 1.0, 1.0], [1.0, 1.0, 0.0], [1.0, 2.0, 0.0], [0.9999999999999999, 2.0, 1.0]], "2": [[1, 1, 0], [2, 1, 0], [2, 2, 0], [1, 2, 0]], "3": [[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.... | q+steps+partial_vis | [
"yes",
"no"
] | |
112_q+steps+all_intermediate_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 1 as the base:
Step 1: Fold face 2 upwards
<image_1>
Step 2: Fold face 3 downwards
<image_2>
Step 3: Fold face 4 downwards towards face 1
<image_3>
Step 4: Fold face 5 inwards towards face 1
<image_4>
Based on the above steps, ca... | A | {"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,... | q+steps+all_intermediate_vis | [
"yes",
"no"
] | |
37_q+steps+all_for_valid_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 2 as the base:
Step 1: Fold face 1 upwards
<image_1>
Step 2: Fold face 4 upwards towards face 1
<image_2>
Step 3: Fold face 3 inwards towards face 2
<image_3>
Step 4: Fold face 5 downwards towards face 1
<image_4>
Step 5: Fold fa... | B | {"initial_net": {"name": "Big T - Variant 1", "faces": {"1": [[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": [[1, 0, 0], [2, 0, 0], [2, 1, 0], [1, 1, 0]], "3": [[2.0, -6.123233995736766e-17, 1.0], [2.0, 0.9999999999999999, 1.0], [2.0, 0.9999999999999999, 1.110223... | q+steps+all_for_valid_vis | [
"no",
"yes"
] | |
16_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "t-shaped Net Variant 1", "faces": {"3": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]], "2": [[-6.123233995736766e-17, 0.0, 1.0], [0.0, 0.0, 0.0], [0.0, 1.0, 0.0], [-6.123233995736766e-17, 1.0, 1.0]], "4": [[1.0, 0.0, 0.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 0.0]], "5": [[1.0, 0.0, 1.0... | q_only | [
"no",
"yes"
] | |
140_q+steps+all_for_valid_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 1 as the base:
Step 1: Fold face 4 upwards
<image_1>
Step 2: Fold face 3 inwards towards face 1
<image_2>
Step 3: Fold face 2 inwards towards face 1
<image_3>
Step 4: Fold face 5 downwards towards face 2
<image_4>
Step 5: Fold fa... | B | {"initial_net": {"name": "1-3-2 Net", "faces": {"1": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]], "2": [[0.0, 1.0, 0.0], [0.0, 1.0, 1.0], [-2.83276944882399e-16, 0.0, 1.0], [-2.83276944882399e-16, 0.0, 0.0]], "3": [[1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [0.0, 1.0, 1.0], [0.0, 1.0, 0.0]], "4": [[1.0, 0.0, 0.0], [1.0, 0.0, 1... | q+steps+all_for_valid_vis | [
"no",
"yes"
] | |
85_q+steps+partial_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 5 as the base:
Step 1: Fold face 6 upwards
<image_1>
Step 2: Fold face 3 inwards towards face 5
Step 3: Fold face 2 upwards towards face 6
Step 4: Fold face 4 upwards towards face 2
Step 5: Fold face 1 inwards towards face 3
Base... | A | {"initial_net": {"name": "2 Rows of 3", "faces": {"1": [[0.9999999999999999, 1.0, 1.0], [1.0, 1.0, 0.0], [1.0, 0.0, -4.978996250514798e-17], [1.0, 0.0, 0.9999999999999999]], "2": [[1.0, 1.0, 0.0], [2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [1.0, 1.0, 1.0]], "3": [[2.0, 1.0, 0.0], [2.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, 0.0... | q+steps+partial_vis | [
"no",
"yes"
] | |
110_q+steps+all_intermediate_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 6 as the base:
Step 1: Fold face 5 upwards
<image_1>
Step 2: Fold face 4 inwards towards face 6
<image_2>
Step 3: Fold face 3 downwards towards face 5
<image_3>
Step 4: Fold face 2 downwards towards face 5
<image_4>
Based on the ... | A | {"initial_net": {"name": "1-3-2 Net", "faces": {"1": [[3.0, -1.0000000000000002, 1.1442377452219691e-17], [2.0, -1.0, 6.123233995736766e-17], [2.0, -0.9999999999999999, 1.0], [3.0, -1.0000000000000002, 1.0000000000000002]], "2": [[3.0, -0.9999999999999999, 1.0], [3.0, 1.224646799147353e-16, 1.0], [3.0000000000000004, 1... | q+steps+all_intermediate_vis | [
"yes",
"no"
] | |
28_q+steps+partial_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 4 as the base:
Step 1: Fold face 3 upwards
<image_1>
Step 2: Fold face 2 downwards
Step 3: Fold face 5 upwards towards face 2
Step 4: Fold face 6 inwards towards face 2
Step 5: Fold face 1 inwards towards face 3
Based on the abov... | A | {"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]]... | q+steps+partial_vis | [
"yes",
"no"
] | |
7_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 6 as the base:
Step 1: Fold face 1 upwards
Step 2: Fold face 2 inwards towards face 6
Step 3: Fold face 3 inwards towards face 6
Step 4: Fold face 4 inwards towards face 1
Step 5: Fold face 5 inwards towards face 1
Based on the ... | A | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=0)", "faces": {"1": [[0.0, 1.0, 0.0], [1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [0.0, 1.0, 1.0]], "2": [[1.0, 1.0, 0.0], [1.0, 0.0, 0.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0]], "3": [[1.0, 0.0, 0.0], [0.0, -2.83276944882399e-16, 0.0], [0.0, -2.83276944882399e-16, 1.0], [1.0, 0... | q+steps | [
"no",
"yes"
] | |
38_q+steps+all_for_valid_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 5 as the base:
Step 1: Fold face 6 upwards
<image_1>
Step 2: Fold face 3 upwards towards face 6
<image_2>
Step 3: Fold face 4 upwards towards face 3
<image_3>
Step 4: Fold face 2 downwards towards face 3
<image_4>
Step 5: Fold fa... | A | {"initial_net": {"name": "Big T - Variant 2", "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, -2.0... | q+steps+all_for_valid_vis | [
"yes",
"no"
] | |
42_q+steps | Check out a net with 6 faces below:
<image_0>Below are the steps to fold the net with face 5 as the base:
Step 1: Fold face 4 upwards
Step 2: Fold face 3 downwards
Step 3: Fold face 2 downwards towards face 5
Step 4: Fold face 1 upwards towards face 4
Step 5: Fold face 6 upwards towards face 2
Based on the above steps... | B | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=0)", "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,... | q+steps | [
"yes",
"no"
] | |
7_q+steps+partial_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 6 as the base:
Step 1: Fold face 1 upwards
<image_1>
Step 2: Fold face 2 inwards towards face 6
<image_2>
Step 3: Fold face 3 inwards towards face 6
Step 4: Fold face 4 inwards towards face 1
Step 5: Fold face 5 inwards towards f... | B | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=0)", "faces": {"1": [[0.0, 1.0, 0.0], [1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [0.0, 1.0, 1.0]], "2": [[1.0, 1.0, 0.0], [1.0, 0.0, 0.0], [1.0, 0.0, 1.0], [1.0, 1.0, 1.0]], "3": [[1.0, 0.0, 0.0], [0.0, -2.83276944882399e-16, 0.0], [0.0, -2.83276944882399e-16, 1.0], [1.0, 0... | q+steps+partial_vis | [
"yes",
"no"
] | |
65_q+steps+partial_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 2 as the base:
Step 1: Fold face 1 upwards
<image_1>
Step 2: Fold face 3 upwards towards face 1
<image_2>
Step 3: Fold face 4 downwards towards face 1
Step 4: Fold face 5 downwards towards face 1
Step 5: Fold face 6 downwards tow... | B | {"initial_net": {"name": "invalid_E", "faces": {"1": [[0.0, 1.0, 0.0], [1.0, 1.0, 0.0], [1.0, 1.0, 1.0], [0.0, 1.0, 1.0]], "6": [[-4.930380657631324e-32, 1.0, 1.0000000000000002], [-2.83276944882399e-16, 1.0, 2.220446049250313e-16], [0.9999999999999997, 1.0, -6.123233995736767e-17], [0.9999999999999999, 1.0, 0.99999999... | q+steps+partial_vis | [
"yes",
"no"
] | |
96_q+steps+all_intermediate_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 1 as the base:
Step 1: Fold face 2 upwards
<image_1>
Step 2: Fold face 3 downwards
<image_2>
Step 4: Fold face 5 upwards towards face 1
Step 5: Fold face 6 upwards towards face 1
Based on the above steps, can the net be folded to... | B | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=4)", "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.... | q+steps+all_intermediate_vis | [
"yes",
"no"
] | |
81_q+steps+all_intermediate_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 3 as the base:
Step 1: Fold face 2 upwards
<image_1>
Step 2: Fold face 4 upwards
<image_2>
Step 3: Fold face 5 upwards towards face 2
<image_3>
Step 5: Fold face 1 downwards towards face 4
Based on the above steps, can the net be... | A | {"initial_net": {"name": "invalid_F", "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], [... | q+steps+all_intermediate_vis | [
"no",
"yes"
] | |
57_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "Big T Net", "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, -6.123233995736766e-17, 1.0],... | q_only | [
"no",
"yes"
] | |
48_q_only | Check out a net with 6 faces below:
<image_0>Can the net be folded to form a cube, yes or no? | B | {"initial_net": {"name": "2 Rows of 3", "faces": {"1": [[3.0, 0.9999999999999998, 1.0], [2.0, 1.0, 1.0], [2.0, 0.9999999999999999, 0.0], [3.0, 0.9999999999999997, 2.220446049250313e-16]], "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": [... | q_only | [
"yes",
"no"
] | |
15_q+steps+all_intermediate_vis | Check out a net with 6 faces below:
<image_0>Here are the steps to fold the net with face 2 as the base:
Step 1: Fold face 1 upwards
<image_1>
Step 2: Fold face 3 upwards
<image_2>
Step 4: Fold face 5 downwards towards face 1
Step 5: Fold face 6 downwards towards face 1
Based on the above steps, can the net be folded ... | A | {"initial_net": {"name": "Net B: Row 5 + Face 6 (shift=3)", "faces": {"1": [[0.9999999999999999, 1.0, 1.0], [1.0, 1.0, 0.0], [1.0, 2.0, 0.0], [0.9999999999999999, 2.0, 1.0]], "2": [[1, 1, 0], [2, 1, 0], [2, 2, 0], [1, 2, 0]], "3": [[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.... | q+steps+all_intermediate_vis | [
"no",
"yes"
] |
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