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Skeletal Cuboctahedron Animation

Skeletal Cuboctahedron Animation
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2020-07-17 00:32
PolygonSolid GeometryTransformationGeometric Construction
In collections Action Modular Origami
This example demonstrates the construction of a skeletal cuboctahedron model folded from paper, consisting of 12 units, inspired by the book 'Action Modular Origami' published by Tarquin. The animation shows the step-by-step folding process of the model. Key mathematical concepts involved include solid geometry, polygon construction, and spatial transformations. The construction utilizes GeoGebra commands and objects such as Line, OrthogonalPlane, Vector, Plane, Rotate, Translate, Midpoint, Dilate, Polygon, OrthogonalLine, Intersect, Angle, and Mirror. It is suitable for high school and above students studying solid geometry, spatial geometry transformations, and for mathematical modeling and geometric construction purposes.

GeoGebra Commands & Parameters

  1. Line(A, B) → lx
  2. OrthogonalPlane(B, lx) → xx
  3. Vector(B, A) → u
  4. Plane(A, B, Bkeep) → zz
  5. Rotate(A, (-(90°)), B, zz) → C
  6. Translate(C, u) → D
  7. Rotate(B, (-(90°)), C, xx) → G
  8. Translate(G, u) → H
  9. Rotate(C, 90°, B, xx) → F
  10. Translate(F, u) → E
  11. Midpoint(C, G) → CG
  12. Midpoint(H, G) → GH
  13. Midpoint(F, G) → FG
  14. Midpoint(A, B) → AB
  15. Midpoint(A, E) → AE
  16. Midpoint(A, D) → AD
  17. Midpoint(B, F) → BF
  18. Midpoint(A, G) → O
  19. Dilate(GH, b, O) → GH'
  20. Dilate(AD, b, O) → AD'
  21. Dilate(BF, b, O) → BF'
  22. Midpoint(D, H) → DH
  23. Dilate(DH, b, O) → DH'
  24. Midpoint(E, H) → EH
  25. Midpoint(C, D) → CD
  26. Midpoint(B, C) → BC
  27. Dilate(BC, b, O) → BC'
  28. Midpoint(E, F) → EF
  29. Dilate(EF, b, O) → EF'
  30. Dilate(CD, b, O) → CD'
  31. Dilate(AE, b, O) → AE'
  32. Dilate(FG, b, O) → FG'
  33. Dilate(EH, b, O) → EH'
  34. Dilate(CG, b, O) → CG'
  35. Dilate(AB, b, O) → AB'
  36. Polygon(AE, BF, CG, DH) → poly1, i, j, k, l
  37. Polygon(AE', EF, FG', CG, CD', AD) → poly2, t, a_1, b_1, c_1, d_1, e_1
  38. Polygon(EH, EF', BF, BC', CD, DH') → poly4, f_1, g_1, h_1, i_1, j_1, k_1
  39. Polygon(GH', FG, BF', AB, AD', DH) → poly5, h, m, n, p, q, r
  40. Polygon(AB, EF, GH, CD) → poly1', i', j', k', l'
  41. Polygon(EH', GH, CG', BC, AB', AE) → poly3, c, d, e, f, g, s
  42. Polygon(AD, BC, FG, EH) → poly1'_1, i'_1, j'_1, k'_1, l'_1
  43. OrthogonalLine(A, zz) → lz
  44. Plane(A, B, F) → yy
  45. OrthogonalLine(A, yy) → l_1
  46. Line(O, lz) → lzz
  47. Line(O, lx) → lxx
  48. Line(O, l_1) → lyy
  49. Rotate(GH, α, lzz) → GH'_1
  50. Rotate(FG, α, lzz) → FG'_1
  51. Rotate(EF, α, lzz) → EF'_1
  52. Rotate(EH, α, lzz) → EH'_1
  53. Polygon(GH', EH'_1, O) → poly6, o, gh', eh'_1
  54. Polygon(FG', GH'_1, O) → poly7, o_1, fg', gh'_1
  55. Polygon(EF', FG'_1, O) → poly8, o_2, ef', fg'_1
  56. Intersect(lyy, lzz) → I
  57. Polygon(EH', EF'_1, O) → poly9, o_3, eh', ef'_1
  58. Rotate(poly9, β, fg'_1) → poly9'
  59. Rotate(poly6, β, ef'_1) → poly6'
  60. Rotate(poly7, β, eh'_1) → poly7'
  61. Rotate(poly8, β, gh'_1) → poly8'
  62. Rotate(poly9, β, ef'_1) → poly9'_1
  63. Rotate(poly6, β, eh'_1) → poly6'_1
  64. Rotate(poly7, β, gh'_1) → poly7'_1
  65. Rotate(poly8, β, fg'_1) → poly8'_1
  66. Rotate(poly7, β, eh'_1) → poly7'_2
  67. Line(AE', CG') → a
  68. Line(DH', BF') → m_1
  69. Rotate(poly6', (-β), a) → poly6''
  70. Rotate(poly6'_1, β, a) → poly10
  71. Rotate(poly9'_1, β, m_1) → poly11
  72. Rotate(poly8', β, a) → poly8''
  73. Rotate(poly9', β, m_1) → poly9''
  74. OrthogonalLine(O, zz) → n_1
  75. Rotate(poly7', (-β), m_1) → poly7''
  76. Rotate(poly7'_1, β, m_1) → poly12
  77. Rotate(poly8'_1, (-β), a) → poly13
  78. Line(O, CD') → p_1
  79. Line(O, EH') → q_1
  80. Rotate(poly9'', (-β), q_1) → poly9'''
  81. Line(O, GH') → r_1
  82. Rotate(poly6'', (-β), r_1) → poly6'''
  83. Rotate(poly12, (-β), r_1) → poly12'
  84. Line(AD', O) → s_1
  85. Rotate(poly13, (-β), s_1) → poly13'
  86. Angle(O, EF', FG'_1, poly8'_1) → γ
  87. Rotate(poly6, δ, lzz) → poly6'_2
  88. Mirror(poly6', lzz) → poly6''_1
  89. Rotate(poly6', δ, lzz) → poly6''_2
  90. Rotate(poly6'', δ, lzz) → poly6'''_1
  91. Rotate(poly6'_1, δ, lzz) → poly14
  92. Rotate(poly10, δ, lzz) → poly10'
  93. Rotate(poly6''', δ, lzz) → poly15
  94. Rotate(poly9'_1, δ, lzz) → poly16
  95. Rotate(poly9, δ, lzz) → poly9'_2
  96. Rotate(poly9', δ, lzz) → poly9''_1
  97. Rotate(poly9'', δ, lzz) → poly9'''_1
  98. Rotate(poly9''', δ, lzz) → poly17
  99. Rotate(poly11, δ, lzz) → poly11'
  100. Rotate(poly7'_1, δ, lzz) → poly18
  101. Rotate(poly7, δ, lzz) → poly7'_3
  102. Rotate(poly7', δ, lzz) → poly7''_1
  103. Rotate(poly7'', δ, lzz) → poly7'''
  104. Rotate(poly12', δ, lzz) → poly12''
  105. Rotate(poly12, δ, lzz) → poly12'_1
  106. Rotate(poly8, δ, lzz) → poly8'_2
  107. Rotate(poly8'_1, δ, lzz) → poly19
  108. Rotate(poly13, δ, lzz) → poly13'_1
  109. Rotate(poly13', δ, lzz) → poly13''
  110. Rotate(poly8'', δ, lzz) → poly8'''
  111. Rotate(poly8', δ, lzz) → poly8''_1

AI Drawing Prompt Reference

Draw an animated skeletal cuboctahedron model folded from paper, showing the step-by-step folding process. The model consists of 12 units inspired by 'Action Modular Origami'. Start by drawing two line segments and their orthogonal planes, then use vectors and rotations to construct key points, followed by translations and reflections to generate midpoints. Finally, connect these points to form multiple polygons, creating a skeletal structure that demonstrates dynamic transformations.
The prompt above was compiled from the original drawing commands and is for reference only.