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All Cube Nets in 3D

All Cube Nets in 3D
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2020-04-29 19:40
PolygonVectorSolid GeometryGeometric Construction
This example demonstrates all possible nets of a cube in three-dimensional space, showing how they can be folded into a cube. It involves core mathematical concepts such as solid geometry, polygon construction, and spatial transformations. Key GeoGebra commands and objects used include Sequence, Point, Sum, If, Vector, Rotate, and Polygon. Suitable for high school students and geometry enthusiasts studying spatial geometry.

GeoGebra Commands & Parameters

  1. Sequence(D + (0, i), i, 0, 10) → LD
  2. Point(LD) → R
  3. Sum(Lc) → sumc
  4. If(n < 8, (-0.5, 0), (-1, -0.5)) → A_0
  5. Vector(A_0, (-0.5, -0.5)) → u
  6. Rotate(B + (2, 1), (t * π / 2), Line[B + (1, 1), B + (1, 0)]) → B1_2
  7. Rotate(B + (2, 2), (t * π / 2), Line[B + (1, 1), B + (1, 0)]) → B1_3
  8. Rotate(B + (1, 0), (t * π / 2), Line[F1_3, F1_4]) → F1_2
  9. Rotate(B, (t * π / 2), Line[F1_3, F1_4]) → F1_1
  10. Polygon(F1_1, F1_2, F1_3, F1_4) → qF1, s011, s012, s013, s014
  11. Rotate(B + (1, 3), (t * π / 2), Line[A1_4, A1_3]) → E1_3
  12. Rotate(B + (0, 3), (t * π / 2), Line[A1_4, A1_3]) → E1_4
  13. Polygon(E1_1, E1_2, E1_3, E1_4) → qE1, e09_1, e09_2, e09_3, e09_4
  14. Polygon(B1_1, B1_2, B1_3, B1_4) → qB1, e06_1, e06_2, e06_3, e06_4
  15. Rotate(C1_1 + Vector[B1_1, C1_1], (t * π / 2), Line[C1_4, C1_1]) → C1_2
  16. Rotate(C1_4 + Vector[B1_1, C1_1], (t * π / 2), Line[C1_4, C1_1]) → C1_3
  17. Polygon(C1_1, C1_2, C1_3, C1_4) → qC1, e07_1, e07_2, e07_3, e07_4
  18. Rotate(D1_1 + Vector[C1_1, D1_1], (t * π / 2), Line[D1_4, D1_1]) → D1_2
  19. Rotate(D1_4 + Vector[C1_1, D1_1], (t * π / 2), Line[D1_4, D1_1]) → D1_3
  20. Polygon(D1_1, D1_2, D1_3, D1_4) → qD1, e08_1, e08_2, e08_3, e08_4
  21. Polygon(A1_1, A1_2, A1_3, A1_4) → qA1, e05_1, e05_2, e05_3, e05_4
  22. Rotate(B1_3 + Vector[B1_2, B1_3], (t * π / 2), Line[B1_4, B1_3]) → E2_3
  23. Rotate(B1_4 + Vector[B1_1, B1_4], (t * π / 2), Line[B1_4, B1_3]) → E2_4
  24. Polygon(E2_1, E2_2, E2_3, E2_4) → qE2, e092_1, e092_2, e092_3, e092_4
  25. Rotate(C1_3 + Vector[C1_2, C1_3], (t * π / 2), Line[C1_4, C1_3]) → E3_3
  26. Rotate(C1_4 + Vector[C1_1, C1_4], (t * π / 2), Line[C1_4, C1_3]) → E3_4
  27. Polygon(E3_1, E3_2, E3_3, E3_4) → qE3, e093_1, e093_2, e093_3, e093_4
  28. Rotate(D1_3 + Vector[D1_2, D1_3], (t * π / 2), Line[D1_4, D1_3]) → E4_3
  29. Rotate(D1_4 + Vector[D1_1, D1_4], (t * π / 2), Line[D1_4, D1_3]) → E4_4
  30. Polygon(E4_1, E4_2, E4_3, E4_4) → qE4, e094_1, e094_2, e094_3, e094_4
  31. Rotate(B1_1 + Vector[B1_4, B1_1], (t * π / 2), Line[B1_2, B1_1]) → F2_1
  32. Rotate(B1_2 + Vector[B1_3, B1_2], (t * π / 2), Line[B1_2, B1_1]) → F2_2
  33. Polygon(F2_1, F2_2, F2_3, F2_4) → qF2, e012_1, e012_2, e012_3, e012_4
  34. If(n ≠ 7, (-2, -1.5), (-2.5, -1.5)) → B_1
  35. Polygon(A7_1, A7_2, A7_3, A7_4) → qA7, e067_1, e067_2, e067_3, e067_4
  36. Rotate(A7_2 + Vector[A7_1, A7_2], (t * π / 2), Line[(0.5, 0.5), (0.5, -0.5)]) → B7_2
  37. Rotate(A7_3 + Vector[A7_4, A7_3], (t * π / 2), Line[(0.5, 0.5), (0.5, -0.5)]) → B7_3
  38. Polygon(B7_1, B7_2, B7_3, B7_4) → qB7, f, g, h, i
  39. Rotate(B7_2 + Vector[B7_1, B7_2], (t * π / 2), Line[B7_3, B7_2]) → C7_2
  40. Rotate(B7_3 + Vector[B7_4, B7_3], (t * π / 2), Line[B7_3, B7_2]) → C7_3
  41. Polygon(C7_1, C7_2, C7_3, C7_4) → qC7, e077_1, e077_2, e077_3, e077_4
  42. Rotate(A7_1 + Vector[A7_4, A7_1], (t * π / 2), Line[A7_2, A7_1]) → F7_1
  43. Rotate(A7_2 + Vector[A7_4, A7_1], (t * π / 2), Line[A7_2, A7_1]) → F7_2
  44. Polygon(F7_1, F7_2, F7_3, F7_4) → qF7, f7_1, f7_2, f7_3, f7_4
  45. Rotate(F7_1 + Vector[F7_2, F7_1], (t * π / 2), Line[F7_1, F7_4]) → D7_1
  46. Rotate(F7_4 + Vector[F7_2, F7_1], (t * π / 2), Line[F7_1, F7_4]) → D7_4
  47. Polygon(D7_1, D7_2, D7_3, D7_4) → qD7, d7_1, d7_2, d7_3, d7_4
  48. Rotate(D7_4 + Vector[D7_2, D7_1], (t * π / 2), Line[D7_1, D7_4]) → E7_4
  49. Rotate(D7_1 + Vector[D7_2, D7_1], (t * π / 2), Line[D7_1, D7_4]) → E7_1
  50. Polygon(E7_1, E7_2, E7_3, E7_4) → qE7, e7_1, e7_2, e7_3, e7_4
  51. Rotate(A7_3 + Vector[A7_2, A7_3], (t * π / 2), Line[A7_4, A7_3]) → E8_3
  52. Rotate(A7_4 + Vector[A7_2, A7_3], (t * π / 2), Line[A7_4, A7_3]) → E8_4
  53. Polygon(E8_1, E8_2, E8_3, E8_4) → qE8, e8_1, e8_2, e8_3, e8_4
  54. Rotate(B7_3 + Vector[B7_2, B7_3], (t * π / 2), Line[B7_4, B7_3]) → E9_3
  55. Rotate(B7_4 + Vector[B7_2, B7_3], (t * π / 2), Line[B7_4, B7_3]) → E9_4
  56. Polygon(E9_1, E9_2, E9_3, E9_4) → qE9, e9_1, e9_2, e9_3, e9_4
  57. Rotate(C7_3 + Vector[C7_2, C7_3], (t * π / 2), Line[C7_4, C7_3]) → E10_3
  58. Rotate(C7_4 + Vector[C7_2, C7_3], (t * π / 2), Line[C7_4, C7_3]) → E10_4
  59. Polygon(E10_1, E10_2, E10_3, E10_4) → qE10, e10_1, e10_2, e10_3, e10_4
  60. Rotate(E9_2 + Vector[E9_4, E9_3], (t * π / 2), Line[E9_3, E9_2]) → C11_2
  61. Rotate(E9_3 + Vector[E9_4, E9_3], (t * π / 2), Line[E9_3, E9_2]) → C11_3
  62. Polygon(C11_1, C11_2, C11_3, C11_4) → qC11, c11_1, c11_2, c11_3, c11_4

AI Drawing Prompt Reference

Display all possible nets of a cube, composed of multiple squares that can be folded into a cube. Start by drawing a plane figure made of several squares, then generate multiple similar nets through rotation and translation, showing how they can fold into a cube. Each net consists of four squares connected by shared edges.
The prompt above was compiled from the original drawing commands and is for reference only.