截锥二十面体

截锥二十面体
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2022-04-25 16:03
所属专题 Archimedean Solids
①本范例演示了截锥二十面体的三维几何图形及其特性;②涉及的核心数学概念包括多边形、立体几何、几何作图;③作图要点——从下方『构造摘要』提炼用到了Polygon(多边形)、Icosahedron(二十面体)、Sphere(球体)、Intersect(相交)、Line(线段)、Rotate(旋转)等GeoGebra命令/对象;④适合高中及以上学生学习和理解复杂三维几何形状的构造与性质。

GeoGebra 命令及参数

  1. Polygon(A, B, 3, xOyPlane) → poly1, f, g, h, C
  2. Icosahedron(poly1, true) → a, D, faceACF, faceAFG, faceADG, faceABD, faceBDH, faceBEH, faceBCE, faceCEI, faceCFI, faceEHK, E, faceEIK, faceIKL, faceFIL, faceHJK, faceJKL, faceGJL, faceFGL, faceDHJ, faceDGJ, edgeAF, F, edgeCF, edgeAG, edgeFG, edgeAD, edgeDG, edgeBD, edgeBH, edgeDH, edgeBE, edgeEH, G, edgeCE, edgeCI, edgeEI, edgeFI, edgeEK, edgeHK, edgeIK, edgeIL, edgeKL, edgeFL, H, edgeJK, edgeHJ, edgeJL, edgeGL, edgeGJ, edgeDJ, I, J, K, L
  3. Sphere(L, d) → c
  4. Intersect(edgeGL, c) → M,
  5. Intersect(edgeFL, c) → N,
  6. Intersect(edgeJL, c) → O,
  7. Intersect(edgeIL, c) → P,
  8. Intersect(edgeKL, c) → Q,
  9. Line(J, C) → i
  10. Polygon(O, Q, P, N, M) → poly2, o, q, p, n, m
  11. Rotate(poly2, -72°, i) → poly2'
  12. Rotate(poly2, -144°, i) → poly2'_{1}
  13. Sphere(B, d) → e
  14. Intersect(edgeBE, e) → R,
  15. Intersect(g, e) → S,
  16. Intersect(edgeBH, e) → T,
  17. Intersect(edgeBD, e) → U,
  18. Intersect(f, e) → V,
  19. Polygon(V, S, R, T, U) → poly3, v, s, r, t, u
  20. Rotate(poly3, 72°, i) → poly3'
  21. Rotate(poly3, 144°, i) → poly3'_{1}
  22. Rotate(poly3, -72°, i) → poly3'_{2}
  23. Sphere(J, d) → j
  24. Intersect(edgeGJ, j) → W,
  25. Intersect(edgeHJ, j) → Z,
  26. Intersect(edgeJK, j) → A_1,
  27. Intersect(edgeJL, j) → B_1,
  28. Intersect(edgeDJ, j) → C_1,
  29. Polygon(W, C_1, Z, A_1, B_1) → poly5, w, c_1, z_1, a_1, b_1
  30. Sphere(C, d) → k
  31. Intersect(g, k) → D_1,
  32. Intersect(h, k) → E_1,
  33. Intersect(edgeCE, k) → F_1,
  34. Intersect(edgeCI, k) → G_1,
  35. Intersect(edgeCF, k) → H_1,
  36. Polygon(F_1, D_1, E_1, H_1, G_1) → poly6, f_1, d_1, e_1, h_1, g_1
  37. Rotate(M, -72°, i) → M'
  38. Rotate(M, -144°, i) → M'_{1}
  39. Rotate(Q, -72°, i) → Q'
  40. Rotate(Q, -144°, i) → Q'_{1}
  41. Rotate(O, -72°, i) → O'
  42. Rotate(O, -144°, i) → O'_{1}
  43. Rotate(P, -72°, i) → P'
  44. Rotate(P, -144°, i) → P'_{1}
  45. Rotate(N, -72°, i) → N'
  46. Rotate(N', -72°, i) → N''
  47. Rotate(N'', -72°, i) → N'''
  48. Polygon(Q'_{3}, P'_{3}, N''', M'_{3}, O'_{3}) → poly7, q'_{3}, p'_{3}, n''', m'_{3}, o'_{3}
  49. Rotate(N''', -72°, i) → I_1
  50. Polygon(Q'_{2}, P'_{2}, I_1, M'_{2}, O'_{2}) → poly8, q'_{2}, p'_{2}, i_1, m'_{2}, o'_{2}
  51. Rotate(R, -72°, i) → R'
  52. Rotate(R, -144°, i) → R'_{1}
  53. Rotate(T, -72°, i) → T'
  54. Rotate(T, -144°, i) → T'_{1}
  55. Rotate(V, -72°, i) → V'
  56. Rotate(V, -144°, i) → V'_{1}
  57. Rotate(V, 72°, i) → V'_{2}
  58. Rotate(V, 144°, i) → V'_{3}
  59. Rotate(V, 72°, i) → V'_{4}
  60. Rotate(V, 144°, i) → V'_{5}
  61. Rotate(V, -72°, i) → V'_{6}
  62. Rotate(V, 72°, i) → V'_{7}
  63. Rotate(S, -72°, i) → S'
  64. Rotate(S, -72°, i) → S'_{1}
  65. Rotate(S, 72°, i) → S'_{2}
  66. Rotate(S'_{2}, 72°, i) → K_1
  67. Rotate(K_1, 72°, i) → L_1
  68. Rotate(poly3'_{2}, -72°, i) → poly4
  69. Polygon(M'_{2}, I_1, U''', T'_{1}, P, Q) → poly9, l, j_1, u''', t'_{1}, p_1, q_1
  70. Rotate(poly9, -72°, i) → poly9'
  71. Rotate(poly9, -144°, i) → poly9'_{1}
  72. Polygon(P'_{3}, T, R, V'_{6}, J_1, N''') → poly10, k_1, t_1, r_1, v'_{6}, l_1, m_1
  73. Rotate(poly10, -72°, i) → poly10'
  74. Rotate(poly10, -144°, i) → poly10'_{1}
  75. Polygon(W, O', M', Q'_{1}, O'_{1}, C_1) → poly11, w_1, o', m', q'_{1}, o'_{1}, n_1
  76. Rotate(poly11, -144°, i) → poly11'
  77. Rotate(poly11, -72°, i) → poly11'_{1}
  78. Polygon(K_1, H_1, E_1, S'_{2}, V'_{7}, R'_{3}) → poly12, s_1, f_2, g_2, s'_{2}, v'_{7}, r'_{3}
  79. Rotate(poly12, 72°, i) → poly12'
  80. Rotate(poly12, -72°, i) → poly12'_{1}
  81. Rotate(poly12'_{1}, 72°, i) → poly13
  82. Rotate(poly11', -72°, i) → poly11''
  83. Rotate(poly11'', -72°, i) → poly11'''
  84. Rotate(poly9'_{1}, -72°, i) → poly14
  85. Rotate(poly14, -72°, i) → poly14'
  86. Rotate(poly12'_{1}, -72°, i) → poly16
  87. Rotate(poly16, -72°, i) → poly16'
  88. Rotate(poly10'_{2}, -72°, i) → poly15
  89. Rotate(poly10, 72°, i) → poly10'_{3}
  90. Rotate(poly10'_{3}, 72°, i) → poly17

AI 绘图提示语参考

绘制一个截锥二十面体,首先创建一个三角形并生成二十面体,然后在其基础上绘制球体并求交点,接着通过旋转和相交操作构建多个五边形,最后将这些五边形组合起来形成截锥二十面体的完整形状。
以上提示语为根据原始绘图命令整理而来,仅供参考。