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Cube – Regular Dodecahedron Origami Animation

Cube – Regular Dodecahedron Origami Animation
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2020-07-17 00:43
PolygonSolid GeometryTransformationGeometric ConstructionSlider Animation
In collections Action Modular Origami
This example demonstrates an animated model of a cube and a regular dodecahedron folded from paper, showcasing the spatial relationships and transformations between polyhedra in solid geometry. The core mathematical concepts include regular polyhedra (cube, regular dodecahedron), rotation, symmetry, and three-dimensional geometric transformations. In terms of construction, the summary reveals the use of GeoGebra commands such as Point, Line, PolyLine, Segment, OrthogonalLine, Intersect, If, Plane, Polygon, Rotate, IntersectPath, and RoofPoly2, along with numerous objects like shift, K_1, T, S, m, g_1, D_2, h_1, Z_1, D_4, E_2, B_2, C_2, A_2, t, clock, rot1s, D, C, cc, A, C_1, B_1, A_1, Z, W, V, p, constClock, U, n, A1, rot1a, constSingle, rot0, bControl, rot1, J_1, I_1, G_1. Sliders control the rotation animation to simulate the folding process dynamically. This example is suitable for senior high school or early university students to understand properties of regular polyhedra, enhance spatial visualization, and learn GeoGebra 3D modeling and animation techniques.

GeoGebra Commands & Parameters

  1. Point(xAxis) → S
  2. Line(S, T) → m
  3. Line(K_1, m) → g_1
  4. Line(D_2, m) → h_1
  5. Point(h_1) → B_2
  6. Point(h_1) → C_2
  7. Point(g_1) → A_2
  8. PolyLine(Z_1, A_2, B_2, C_2, D_4, E_2) → t
  9. Segment(C, D) → cc
  10. Point(h_1) → A_1
  11. Point(h_1) → Z
  12. Point(g_1) → W
  13. PolyLine(V, W, Z, A_1, B_1, C_1) → p
  14. OrthogonalLine(U, m) → n
  15. Intersect(n, p) → A1
  16. If(bControl ≟ constSingle, rot0, If[bControl ≟ constClock, rot1a, rot1s]) → rot1
  17. Point(h_1) → G_1
  18. Point(g_1) → F_1
  19. Point(t) → H_1
  20. PolyLine(E_1, F_1, G_1, H_1, I_1, J_1) → q
  21. Intersect(n, q) → A2
  22. Point(h_1) → O_1
  23. Point(h_1) → N_1
  24. Point(g_1) → M_1
  25. PolyLine(L_1, M_1, N_1, O_1, P_1, Q_1) → r
  26. Intersect(n, r) → A3
  27. Point(h_1) → U_1
  28. Point(h_1) → T_1
  29. Point(g_1) → S_1
  30. PolyLine(R_1, S_1, T_1, U_1, V_1, W_1) → s
  31. Intersect(n, s) → A4
  32. Intersect(n, t) → A5
  33. Segment(D, A) → dd
  34. Plane(B, C, D) → e
  35. Segment(A, B) → aa
  36. Segment(B, C) → bb
  37. If(bControl ≟ constSingle, rot0, If[bControl ≟ constClock, rot4a, rot4s]) → rot4
  38. Polygon(A, B, C, D) → poly1, a, b, c, d
  39. Rotate(B, (-rot1), cc) → B'
  40. Rotate(C, (-rot1), cc) → C'
  41. Rotate(D, (-rot1), cc) → D'
  42. Rotate(A, (-rot1), cc) → A'
  43. Polygon(A', B', C', D') → poly1', a', b', c', d'
  44. If(bControl ≟ constSingle, rot0, If[bControl ≟ constClock, rot2a, rot2s]) → rot2
  45. Rotate(poly1', rot2, b') → poly1''
  46. Rotate(D', rot2, b') → D''
  47. Rotate(A', rot2, b') → A''
  48. Segment(B', A'') → f
  49. If(bControl ≟ constSingle, rot0, If[bControl ≟ constClock, rot3a, rot3s]) → rot3
  50. Rotate(poly1'', rot3, f) → poly1'''
  51. Rotate(D'', rot3, f) → D'''
  52. Rotate(C', rot3, f) → C'''
  53. Segment(A'', D''') → g
  54. Rotate(poly1''', (-rot4), g) → poly2
  55. Rotate(C''', (-rot4), g) → C''''
  56. Rotate(B', (-rot4), g) → B'''
  57. Segment(D''', C'''') → h
  58. If(bControl ≟ constSingle, rot0, If[bControl ≟ constClock, rot5a, rot5s]) → rot5
  59. Rotate(A'', rot5, h) → A'''
  60. Rotate(B''', rot5, h) → B''''
  61. Rotate(e, gable, dd) → e'_3
  62. Rotate(e, (-roof), aa) → e'_1
  63. IntersectPath(e'_3, e'_1) → i
  64. Rotate(e, gable, bb) → e'
  65. IntersectPath(e', e'_1) → j
  66. Rotate(e, (-roof), cc) → e'_2
  67. IntersectPath(e'_3, e'_2) → k
  68. IntersectPath(e', e'_2) → l
  69. Intersect(l, k) → E
  70. Intersect(j, i) → F
  71. RoofPoly2(A, B, C, D, gable, roof) → G, H, poly3, poly4, poly5, poly6, poly7
  72. RoofPoly2(A', D, C, B', gable, roof) → I, J, poly8, poly9, poly10, poly11, poly12
  73. RoofPoly2(C''', B', A'', D''', gable, roof) → K, L, poly13, poly14, poly15, poly16, poly17
  74. RoofPoly2(A''', D''', C'''', B'''', gable, roof) → M, N, poly18, poly19, poly20, poly21, poly22
  75. RoofPoly2(C, D'', A'', B', gable, roof) → O, P, poly23, poly24, poly25, poly26, poly27
  76. RoofPoly2(A'', B''', C'''', D''', gable, roof) → Q, R, poly28, poly29, poly30, poly31, poly32
  77. Line(D_1, m) → f_1

AI Drawing Prompt Reference

Create an animated model of a cube and a regular dodecahedron folded from paper, demonstrating spatial relationships and transformations between the polyhedra in solid geometry. The model simulates the folding process dynamically with rotation and symmetry, controlled by a slider. Begin by constructing basic geometric elements like points and lines, then form polygons and polylines, determine key positions using orthogonal lines and intersections, and finally achieve the final 3D model through rotations and transformations.
The prompt above was compiled from the original drawing commands and is for reference only.