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菱形十二面体的分解 by מכון דוידסון לחינוך מדעי

菱形十二面体的分解 by מכון דוידסון לחינוך מדעי
几何画板及绘图内容加载中，请稍等……
2015-02-19 19:35
多边形立体几何几何作图
本范例展示了菱形十二面体如何分解为一个立方体和多个四面体，适合使用红蓝3D眼镜观察。它涉及立体几何中的基本概念，如多面体的分解与重组。通过使用GeoGebra命令如Segment, Plane, Polygon等，可以直观地展示几何作图的过程。适合初中及以上学生学习立体几何。

GeoGebra 命令及参数

  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 绘图提示语参考

画一个由立方体和多个金字塔组成的菱形十二面体分解图，展示其如何分解和重组，适合用红蓝3D眼镜观察。先画出立方体和金字塔的基本形状，然后连接它们的边和顶点，形成完整的分解结构，最后用不同颜色区分各个部分，突出几何构造过程。
以上提示语为根据原始绘图命令整理而来，仅供参考。