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Animated Decomposition of the Rhombic Dodecahedron by מכון דוידסון לחינוך מדעי

Animated Decomposition of the Rhombic Dodecahedron by מכון דוידסון לחינוך מדעי
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2015-02-22 13:22
PolygonSolid GeometryGeometric Construction
This example demonstrates the animated decomposition of a rhombic dodecahedron into a cube and pyramids. It involves core mathematical concepts such as polygons, solid geometry, angles, and transformations. The construction utilizes GeoGebra commands like If, Polygon, Segment, and objects including 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'. It is suitable for high school and above students to learn and understand the geometric principles of polyhedral decomposition and combination, as well as for mathematical teaching demonstrations.

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 showing the decomposition of a rhombic dodecahedron into a cube and pyramids, highlighting core mathematical concepts like polygons, solid geometry, angles, and transformations. Begin by constructing the rhombic dodecahedron, then animate its decomposition into a cube and multiple pyramids, demonstrating the process of breaking down and combining polyhedra for high school and above students to understand geometric principles of polyhedral decomposition and combination.
The prompt above was compiled from the original drawing commands and is for reference only.