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Animated Decomposition of the Rhombic Dodecahedron

Animated Decomposition of the Rhombic Dodecahedron
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2015-02-22 13:26
Solid GeometryGeometric Construction
This example demonstrates the animated decomposition of a rhombic dodecahedron into a cube and pyramids. It involves core mathematical concepts such as solid geometry, transformation, and geometric construction. The construction uses GeoGebra commands like If, Polygon, Segment, and objects like X, A3, Alpha, v1, K, u1, C, A, A2, A1, H, C', J, B, E, F, G, L, M, N, I, D, M', J', F', poly2, k_1, l_1, m_1, poly4, n_1, p_1, q_1, poly5, h_2, m', j', poly6, j'_1, c'. Suitable for high school and above learning solid geometry and geometric construction.

GeoGebra Commands & Parameters

  1. If(X < 0.35, 1, If[X < 0.65, (-20 * X / 3) + 10 / 3, -1]) → A3
  2. Polygon(F', C', H) → poly2, k_1, l_1, m_1
  3. Polygon(F', M', H) → poly4, n_1, p_1, q_1
  4. Polygon(M', J', H) → poly5, h_2, m', j'
  5. Polygon(C', H, J') → poly6, j'_1, c', h_3
  6. Polygon(L', I', G) → poly10, g_3, l', i'
  7. Polygon(I', B', G) → poly14, g_4, i'_1, b'_1
  8. Polygon(L', E', G) → poly15, g_5, l'_1, e'_1
  9. Segment(A', B'') → i
  10. Polygon(J'', M'', N') → poly1, n', j'', m''
  11. Polygon(M'', L'', N') → poly7, n'_1, m''_1, l''
  12. Polygon(I'', L'', N') → poly11, n'_2, i'', l''_1
  13. Polygon(J'', I'', N') → poly12, n'_3, j''_1, i''_1
  14. Polygon(C'', F'', A') → poly17, a', c'', f''
  15. Polygon(F'', E'', A') → poly18, a'_1, f''_1, e''
  16. Polygon(E'', B'', A') → poly19, a'_2, e''_1, b''
  17. Polygon(C'', A', B'') → poly20, b''_1, c''_1, a'_3
  18. Polygon(I''', B''', D') → poly21, d', i''', b'''
  19. Polygon(J''', I''', D') → poly22, d'_1, j''', i'''_1
  20. Polygon(B''', C''', D') → poly23, d'_2, b'''_1, c'''
  21. Polygon(C''', D', J''') → poly24, j'''_1, c'''_1, d'_3
  22. Polygon(K', E''', F''') → poly25, f''', k', e'''
  23. Polygon(K', M''', F''') → poly26, f'''_1, k'_1, m'''
  24. Polygon(L''', E''', K') → poly27, k'_2, l''', e'''_1
  25. Polygon(M''', L''', K') → poly28, k'_3, m'''_1, l'''_1
  26. Segment(C, B) → i_2
  27. Segment(C, J) → j_2
  28. Segment(J, M) → l_2
  29. Segment(F, M) → n_2
  30. Segment(C, F) → a_3
  31. Segment(F, E) → c_3
  32. Segment(B, E) → d_3
  33. Segment(B, I) → f_3
  34. Segment(I, L) → j_3
  35. Segment(E, L) → m_3
  36. Segment(M, L) → n_3
  37. Segment(J, I) → p_3
  38. Polygon(B', E', G) → poly3, g, b', e'

AI Drawing Prompt Reference

Create an animated visualization of a rhombic dodecahedron decomposing into a cube and pyramids, showcasing core concepts in solid geometry, transformation, and geometric construction with a clear animated decomposition process.
The prompt above was compiled from the original drawing commands and is for reference only.