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Skeletal Cube – Rhombic Dodecahedron Origami Animation

Skeletal Cube – Rhombic Dodecahedron Origami Animation
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2020-07-17 00:43
PolygonSolid GeometryTransformationGeometric ConstructionSlider Animation
In collections Action Modular Origami
① This example demonstrates a 'skeletal cube' model folded from paper, whose unfolded form is a rhombic dodecahedron, with an animation showing the folding and unfolding process. ② Core mathematical concepts involve solid geometry of polyhedra (rhombic dodecahedron), spatial transformations (rotation and translation), and parametric animation control, also implying symmetry and topological structure. ③ Construction highlights: from the construction summary, GeoGebra commands such as Point, Line, PolyLine, Segment, OrthogonalLine, Intersect, If, Plane, Polygon, Rotate, IntersectPath, RoofPoly2 are used, along with 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 (rot1, rot0) and a clock control the rotation animation. ④ Suitable for upper secondary to early university solid geometry teaching, as well as origami mathematics or dynamic geometry demonstrations, helping students intuitively understand spatial structure and transformations of polyhedra.

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

Draw a skeletal cube model folded from a rhombic dodecahedron, with an animation showing the folding and unfolding process. The figure includes a cubic framework composed of rhombic faces, with rotation and translation transformations. Show auxiliary lines, intersection points, and sliders controlling the animation. Emphasize symmetry and spatial structure, suitable for educational demonstration.
The prompt above was compiled from the original drawing commands and is for reference only.