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Decomposition of Rhombic Dodecahedron

Decomposition of Rhombic Dodecahedron
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2015-02-19 19:33
PolygonSolid GeometryGeometric Construction
This example demonstrates how a rhombic dodecahedron can be decomposed into a cube and several pyramids. Key mathematical concepts include the decomposition of polyhedra in solid geometry. Using GeoGebra commands such as Segment, Plane, Polygon, etc., the construction process of the polyhedron can be visually understood. Suitable for students at the junior high school level and above.

GeoGebra Commands & Parameters

  1. Segment(L, N) → e
  2. Segment(M, N) → f
  3. Segment(M, K) → j
  4. Segment(L, K) → k
  5. Segment(N, I) → g
  6. Segment(K, E) → h
  7. Segment(I, D) → n
  8. Segment(C, D) → p
  9. Segment(C, A) → q
  10. Segment(N, J) → r
  11. Segment(K, F) → d_1
  12. Segment(D, J) → s
  13. Plane(C, F, B) → o
  14. OrthogonalLine(A, o) → f_1
  15. OrthogonalLine(B, o) → g_1
  16. Segment(B, D) → m
  17. Segment(H, C') → h_1
  18. Segment(M', H) → t
  19. Segment(J', H) → a_1
  20. Segment(H, F') → e_1
  21. Polygon(F', C', H) → poly2, k_1, l_1, m_1
  22. Polygon(K, M, F) → poly3, f_2, k_2, m_2
  23. Polygon(F', M', H) → poly4, n_1, p_1, q_1
  24. Polygon(M', J', H) → poly5, h_2, m', j'
  25. Polygon(C', H, J') → poly6, j'_1, c', h_3
  26. Polygon(C, J, D) → poly8, r_1, s_1, t_1
  27. Segment(G, E') → b
  28. Segment(B', G) → d
  29. Segment(G, L') → a
  30. Segment(G, I') → c
  31. Polygon(E', B', G) → poly9, g_2, e', b'
  32. Polygon(L', I', G) → poly10, g_3, l', i'
  33. Polygon(I, B, D) → poly13, d_2, i_3, b_3
  34. Polygon(I', B', G) → poly14, g_4, i'_1, b'_1
  35. Polygon(L', E', G) → poly15, g_5, l'_1, e'_1
  36. Polygon(L, E, K) → poly16, k_3, l_3, e_3
  37. Line(A, N) → c_1
  38. Line(C', c_1) → i_1
  39. Line(B, c_1) → j_1
  40. Line(E, c_1) → a_2
  41. Plane(C', F, B) → o_1
  42. OrthogonalLine(A, o_1) → b_2
  43. OrthogonalLine(C'', o_1) → e_2
  44. Plane(C, F', E') → u_1
  45. OrthogonalLine(E', u_1) → p_2
  46. Segment(C'', A') → c_2
  47. Segment(A', B'') → i
  48. Segment(A', E'') → l
  49. Segment(F'', A') → b_1
  50. Segment(N', M'') → q_2
  51. Segment(N', J'') → r_2
  52. Segment(N', I'') → s_2
  53. Segment(N', L'') → t_2
  54. Polygon(J'', M'', N') → poly1, n', j'', m''
  55. Polygon(M'', L'', N') → poly7, n'_1, m''_1, l''
  56. Polygon(I'', L'', N') → poly11, n'_2, i'', l''_1
  57. Polygon(J'', I'', N') → poly12, n'_3, j''_1, i''_1
  58. Polygon(C'', F'', A') → poly17, a', c'', f''
  59. Polygon(F'', E'', A') → poly18, a'_1, f''_1, e''
  60. Polygon(E'', B'', A') → poly19, a'_2, e''_1, b''
  61. Polygon(C'', A', B'') → poly20, b''_1, c''_1, a'_3
  62. Polygon(I''', B''', D') → poly21, d', i''', b'''
  63. Polygon(J''', I''', D') → poly22, d'_1, j''', i'''_1
  64. Polygon(B''', C''', D') → poly23, d'_2, b'''_1, c'''
  65. Polygon(C''', D', J''') → poly24, j'''_1, c'''_1, d'_3
  66. Polygon(K', E''', F''') → poly25, f''', k', e'''
  67. Polygon(K', M''', F''') → poly26, f'''_1, k'_1, m'''
  68. Polygon(L''', E''', K') → poly27, k'_2, l''', e'''_1
  69. Polygon(M''', L''', K') → poly28, k'_3, m'''_1, l'''_1
  70. Segment(C, F) → i_2
  71. Segment(F, M) → j_2
  72. Segment(M, J) → l_2
  73. Segment(J, C) → n_2
  74. Segment(C, B) → a_3
  75. Segment(B, E) → c_3
  76. Segment(E, L) → d_3
  77. Segment(L, I) → f_3
  78. Segment(I, B) → j_3
  79. Segment(J, I) → m_3
  80. Segment(F, E) → n_3
  81. Segment(M, L) → p_3
  82. Segment(F', M') → q_3
  83. Segment(M', J') → r_3
  84. Segment(J', C') → s_3
  85. Segment(C', F') → t_3
  86. Segment(J''', I''') → a_4
  87. Segment(B''', I''') → b_4
  88. Segment(B''', C''') → c_4
  89. Segment(C''', J''') → d_4
  90. Segment(C'', F'') → e_4
  91. Segment(E'', F'') → f_4
  92. Segment(E'', B'') → h_4
  93. Segment(B'', C'') → i_4
  94. Segment(B', I') → j_4
  95. Segment(I', L') → k_4
  96. Segment(E', L') → l_4
  97. Segment(E', B') → m_4
  98. Segment(E''', L''') → n_4
  99. Segment(L''', M''') → p_4
  100. Segment(M''', F''') → q_4
  101. Segment(E''', F''') → r_4
  102. Segment(J'', M'') → s_4
  103. Segment(L'', M'') → t_4
  104. Segment(L'', I'') → a_5
  105. Segment(I'', J'') → b_5

AI Drawing Prompt Reference

Draw a rhombic dodecahedron, showing how it decomposes into a cube and several pyramids. Start by sketching the edges of the cube, then create the bases and sides of the pyramids, ensuring their vertices align with those of the cube. Use distinct colors or textures to differentiate the cube from the pyramids for a clear visual decomposition.
The prompt above was compiled from the original drawing commands and is for reference only.