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3D Magic Star Animation

3D Magic Star Animation
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2020-07-17 00:33
PolygonVectorSolid GeometryGeometric Construction
In collections Action Modular Origami
This example demonstrates an animated 3D model of a magic star folded from paper, as described in the book 'Action Modular Origami'. It involves core mathematical concepts such as solid geometry, transformations, polygons, and vectors. The construction utilizes GeoGebra commands and objects like Rotate, Polygon, Intersect, Line, OrthogonalLine, Vector, Translate, Point, Dilate, and Sequence. Suitable for high school students and above to learn about 3D shapes and transformations, or for mathematical education purposes.

GeoGebra Commands & Parameters

  1. Rotate(F, (-(45°)), F) → F'_1
  2. Rotate(C, (-(45°)), F) → C'_1
  3. Rotate(E, (-(45°)), F) → E'_1
  4. Rotate(D, (-(45°)), F) → D'_1
  5. Polygon(C'_1, D'_1, E'_1, F'_1) → poly1'_1, c'_1, d'_1, e'_1, f'_1
  6. Polygon(C, D, E, F) → poly1, c, d, e, f
  7. Intersect(e, d'_1) → W
  8. Intersect(d, d'_1) → V
  9. Intersect(xAxis, yAxis) → A
  10. Line(A, B) → a
  11. OrthogonalLine(F, a) → b
  12. Rotate(a, α / 2, A) → a'
  13. Intersect(a', b) → H
  14. Vector(F, H) → u
  15. Translate(V, u) → V'
  16. Translate(W, u) → W'
  17. Translate(F, u) → F'
  18. Translate(D, u) → D'
  19. Translate(C, u) → C'
  20. Point(a') → U
  21. Dilate(U, fac, A) → U'
  22. Translate(E, u) → E'
  23. Polygon(C', D', V', W', F') → poly1', g, h, a_1, b_1, c_1
  24. Vector(A, G) → v
  25. Translate(C', v) → C''
  26. Translate(D', v) → D''
  27. Translate(E', v) → E''
  28. Translate(F', v) → F''
  29. Polygon(C'', D'', E'', F'') → poly1'', c'', d'', e'', f''
  30. Rotate(C'', α, A) → C'''_1
  31. Rotate(D'', α, A) → D'''_1
  32. Rotate(E'', α, A) → E'''_1
  33. Rotate(F'', α, A) → F'''_1
  34. Polygon(C'''_1, D'''_1, E'''_1, F'''_1) → poly1'''_1, c''', d''', e''', f'''
  35. Rotate(C'', (2 * α), A) → C'''_2
  36. Rotate(D'', (2 * α), A) → D'''_2
  37. Rotate(E'', (2 * α), A) → E'''_2
  38. Rotate(F'', (2 * α), A) → F'''_2
  39. Polygon(C'''_2, D'''_2, E'''_2, F'''_2) → poly1'''_2, c'''_1, d'''_1, e'''_1, f'''_1
  40. Rotate(C'''_1, (2 * α), A) → I
  41. Rotate(D'''_1, (2 * α), A) → J
  42. Rotate(E'''_1, (2 * α), A) → K
  43. Rotate(F'''_1, (2 * α), A) → L
  44. Polygon(I, J, K, L) → poly2, i, j, k, l
  45. Rotate(C'', (4 * α), A) → C'''_3
  46. Rotate(D'', (4 * α), A) → D'''_3
  47. Rotate(E'', (4 * α), A) → E'''_3
  48. Rotate(F'', (4 * α), A) → F'''_3
  49. Polygon(C'''_3, D'''_3, E'''_3, F'''_3) → poly1'''_3, c'''_2, d'''_2, e'''_2, f'''_2
  50. Rotate(C'''_1, (4 * α), A) → M
  51. Rotate(D'''_1, (4 * α), A) → N
  52. Rotate(E'''_1, (4 * α), A) → O
  53. Rotate(F'''_1, (4 * α), A) → P
  54. Polygon(M, N, O, P) → poly3, m, n, o, p
  55. Rotate(C'', (6 * α), A) → C'''
  56. Rotate(D'', (6 * α), A) → D'''
  57. Rotate(E'', (6 * α), A) → E'''
  58. Rotate(F'', (6 * α), A) → F'''
  59. Polygon(C''', D''', E''', F''') → poly1''', c'''_3, d'''_3, e'''_3, f'''_3
  60. Rotate(C'''_1, (6 * α), A) → Q
  61. Rotate(D'''_1, (6 * α), A) → R
  62. Rotate(E'''_1, (6 * α), A) → S
  63. Rotate(F'''_1, (6 * α), A) → T
  64. Polygon(Q, R, S, T) → poly4, q, r, s, t
  65. Translate(V', v) → V''
  66. Translate(W', v) → W''
  67. Polygon(C'', D'', V'', W'', F'') → polyPiece, c''_1, d''_1, v'', w'', f''_1
  68. Sequence(Polygon[Rotate[C'', ((2 * n) * α), A], Rotate[D'', ((2 * n) * α), A], Rotate[V'', ((2 * n) * α), A], Rotate[W'', ((2 * n) * α), A], Rotate[F'', ((2 * n) * α), A]], n, 0, 3, 1) → ListPoly1
  69. Sequence(Polygon[Rotate[C'', α + ((2 * n) * α), A], Rotate[D'', α + ((2 * n) * α), A], Rotate[V'', α + ((2 * n) * α), A], Rotate[W'', α + ((2 * n) * α), A], Rotate[F'', α + ((2 * n) * α), A]], n, 0, 3, 1) → ListPoly2
  70. Vector(A, A') → w
  71. Translate(I, w) → I'
  72. Translate(J, w) → J'
  73. Polygon(J, J', I', I) → polySide, j_1, j', i', i_1
  74. Sequence(Rotate[polySide, α + ((2 * n) * α), A], n, 0, 3, 1) → ListPolySide1
  75. Sequence(Rotate[polySide, ((2 * n) * α), A], n, 0, 3, 1) → ListPolySide2
  76. Polygon(Q, R, V'', D'') → polyThin, q_1, r_1, v''_1, d''_2
  77. Polygon(F'', W'', V'', D'', C'') → poly6, f''_2, w''_1, v''_2, d''_3, c''_2
  78. Rotate(F'', (-α), A) → F'''_4
  79. Rotate(W'', (-α), A) → W'''
  80. Rotate(V'', (-α), A) → V'''
  81. Rotate(D'', (-α), A) → D'''_4
  82. Rotate(C'', (-α), A) → C'''_4
  83. Polygon(F'''_4, W''', V''', D'''_4, C'''_4) → poly6', f'''_4, w''', v''', d'''_4, c'''_4
  84. OrthogonalLine(F'''_1, c''_2) → f_1
  85. Intersect(f_1, v''_1) → Z
  86. Polygon(F'', W'', V'', Z, F'''_1) → poly7, f''_3, w''_2, v''_3, z_1, f'''_5
  87. Rotate(F'', α, A) → F'''_5
  88. Rotate(W'', α, A) → W'''_1
  89. Rotate(V'', α, A) → V'''_1
  90. Rotate(Z, α, A) → Z'
  91. Rotate(F'''_1, α, A) → A_1
  92. Polygon(F'''_5, W'''_1, V'''_1, Z', A_1) → polyFat, f'''_6, w'''_1, v'''_1, z', a_2
  93. Sequence(Polygon[Rotate[Q, ((2 * n) * α), A], Rotate[R, ((2 * n) * α), A], Rotate[V'', ((2 * n) * α), A], Rotate[D'', ((2 * n) * α), A]], n, 0, 3, 1) → ListPolyThin2
  94. Sequence(Polygon[Rotate[Q, α + ((2 * n) * α), A], Rotate[R, α + ((2 * n) * α), A], Rotate[V'', α + ((2 * n) * α), A], Rotate[D'', α + ((2 * n) * α), A]], n, 0, 3, 1) → ListPolyThin1
  95. Sequence(Polygon[Rotate[F'''_5, α + ((2 * n) * α), A], Rotate[W'''_1, α + ((2 * n) * α), A], Rotate[V'''_1, α + ((2 * n) * α), A], Rotate[Z', α + ((2 * n) * α), A], Rotate[A_1, α + ((2 * n) * α), A]], n, 0, 3, 1) → ListPolyFat1
  96. Sequence(Polygon[Rotate[F'''_5, ((2 * n) * α), A], Rotate[W'''_1, ((2 * n) * α), A], Rotate[V'''_1, ((2 * n) * α), A], Rotate[Z', ((2 * n) * α), A], Rotate[A_1, ((2 * n) * α), A]], n, 0, 3, 1) → ListPolyFat2
  97. Translate(ListPolyFat1, w) → ListPolyFat1'
  98. Translate(ListPolyThin2, w) → ListPolyThin2'
  99. Translate(ListPolyThin1, w) → ListPolyThin1'
  100. Translate(ListPolyFat2, w) → ListPolyFat2'

AI Drawing Prompt Reference

Create a 3D magic star origami animation by first constructing a regular hexagon, then rotating its vertices around a point to generate new vertices. Next, use these vertices to form new polygons, creating the 3D structure of the magic star. Finally, rotate these polygons around the center point to create an animation effect.
The prompt above was compiled from the original drawing commands and is for reference only.