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二十面体星形构造

二十面体星形构造
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2018-10-25 00:55
多边形立体几何几何作图
①本范例演示了如何通过二十面体的几何特性构建星形多边形；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——使用了Icosahedron（二十面体）、Centroid（重心）、Intersect（相交）、Polygon（多边形）等GeoGebra命令与对象；④适合高中及以上学生学习和教师教学使用，可用于立体几何和几何作图的演示与探究。

GeoGebra 命令及参数

  1. Icosahedron((1, 0, 0), (0, 1, 0), zAxis) → b, A, J, Fläche1, Fläche3, Fläche5, Fläche4, Fläche2, Fläche7, Fläche8, Fläche6, FlächeACG, B, FlächeADG, FlächeCFI, FlächeCGI, FlächeGIJ, FlächeDGJ, FlächeFHI, FlächeHIJ, FlächeEHJ, FlächeDEJ, FlächeBFH, C, FlächeBEH, Kante2, Kante1, Kante6, Kante4, KanteAD, Kante5, KanteDE, Kante3, KanteBE, D, Kante7, Kante9, KanteBF, Kante8, KanteCF, KanteAC, KanteAG, KanteCG, KanteDG, KanteCI, E, KanteFI, KanteGI, KanteGJ, KanteIJ, KanteDJ, KanteHI, KanteFH, KanteHJ, KanteEJ, KanteEH, F, KanteBH, G, H, I
  2. Centroid(Fläche1) → S1
  3. Intersect(Kante1, Kante2) → K
  4. Intersect(yAxis, Kante9) → L
  5. Polygon(K, P1, L) → d1, l, k, p1
  6. Polygon(P1, A, L) → d2, l_1, f, a_1
  7. Polygon(P1, K, A) → d3, a_2, g, k_1
  8. Centroid(Fläche2) → S2
  9. Polygon(B, P2, L) → d4, l_2, b_1, p2
  10. Polygon(P2, K, L) → d5, l_3, h, k_2
  11. Polygon(K, P2, B) → d6, b_2, k_3, i
  12. Centroid(Fläche3) → S3
  13. Polygon(A, P3, D) → d7, d, a_3, p3
  14. Polygon(P3, A, K) → d8, k_4, j, a_4
  15. Polygon(P3, K, D) → d9, d_1, m, k_5
  16. Centroid(Fläche4) → S4
  17. Polygon(E, P4, B) → d10, b_3, e, p4
  18. Polygon(K, P4, E) → d11, e_1, k_6, n
  19. Polygon(K, B, P4) → d12, p, k_7, b_4
  20. Centroid(Fläche5) → S5
  21. Polygon(D, P5, E) → d13, e_2, d_2, p5
  22. Polygon(P5, K, E) → d14, e_3, q, k_8
  23. Polygon(P5, K, D) → d15, d_3, r, k_9
  24. Centroid(Fläche6) → S6
  25. Polygon(L, P6, C) → d16, c, l_4, p6
  26. Polygon(P6, A, C) → d17, c_1, s, a_5
  27. Polygon(L, A, P6) → d18, t, l_5, a_6
  28. Centroid(Fläche7) → S7
  29. Polygon(B, P7, F) → d19, f_1, b_5, p7
  30. Polygon(P7, L, F) → d20, f_2, g_1, l_6
  31. Polygon(P7, B, L) → d21, l_7, h_1, b_6
  32. Centroid(Fläche8) → S8
  33. Polygon(F, P8, C) → d22, c_2, f_3, p8
  34. Polygon(P8, L, C) → d23, c_3, i_1, l_8
  35. Polygon(P8, F, L) → d24, l_9, j_1, f_4
  36. Centroid(FlächeACG) → S9
  37. Polygon(C, P9, G) → d25, g_2, c_4, p9
  38. Polygon(C, A, P9) → d26, m_1, c_5, a_7
  39. Polygon(P9, A, G) → d27, g_3, n_1, a_8
  40. Centroid(FlächeADG) → S10
  41. Polygon(G, P10, D) → d28, d_4, g_4, p10
  42. Polygon(P10, G, A) → d29, a_9, p_1, g_5
  43. Polygon(P10, A, D) → d30, d_5, q_1, a_{10}
  44. Centroid(FlächeBEH) → S11
  45. Polygon(E, P11, H) → d31, h_2, e_4, p11
  46. Polygon(E, B, P11) → d32, r_1, e_5, b_7
  47. Polygon(B, H, P11) → d33, s_1, b_8, h_3
  48. Centroid(FlächeBFH) → S12
  49. Polygon(H, P12, F) → d34, f_5, h_4, p12
  50. Polygon(B, P12, H) → d35, h_5, b_9, t_1
  51. Polygon(B, F, P12) → d36, i_2, b_{10}, f_6
  52. Centroid(FlächeCFI) → S13
  53. Polygon(F, P13, I) → d37, i_3, f_7, p13
  54. Polygon(F, C, P13) → d38, j_2, f_8, c_6
  55. Polygon(P13, C, I) → d39, i_4, m_2, c_7
  56. Centroid(FlächeCGI) → S14
  57. Polygon(I, P14, G) → d40, g_6, i_5, p14
  58. Polygon(P14, C, G) → d41, g_7, n_2, c_8
  59. Polygon(C, P14, I) → d42, i_6, c_9, p_2
  60. Centroid(FlächeDEJ) → S15
  61. Polygon(J, P15, E) → d43, e_6, j_3, p15
  62. Polygon(P15, D, E) → d44, e_7, q_2, d_6
  63. Polygon(J, D, P15) → d45, r_2, j_4, d_7
  64. Centroid(FlächeDGJ) → S16
  65. Polygon(P16, D, J) → d46, j_5, p16, d_8
  66. Polygon(P16, G, D) → d47, d_9, s_2, g_8
  67. Polygon(P16, J, G) → d48, g_9, t_2, j_6
  68. Centroid(FlächeEHJ) → S17
  69. Polygon(J, P17, H) → d49, h_6, j_7, p17
  70. Polygon(P17, E, H) → d50, h_7, m_3, e_8
  71. Polygon(P17, J, E) → d51, e_9, n_3, j_8
  72. Centroid(FlächeFHI) → S18
  73. Polygon(H, P18, I) → d52, i_7, h_8, p18
  74. Polygon(P18, F, I) → d53, i_8, p_3, f_9
  75. Polygon(P18, H, F) → d54, f_{10}, q_3, h_9
  76. Centroid(FlächeGIJ) → S19
  77. Polygon(I, P19, J) → d55, j_9, i_9, p19
  78. Polygon(P19, G, J) → d56, j_{10}, r_3, g_{10}
  79. Polygon(P19, I, G) → d57, g_{11}, s_3, i_{10}
  80. Centroid(FlächeHIJ) → S20
  81. Polygon(H, P20, J) → d58, j_{11}, h_{10}, p20
  82. Polygon(P20, I, J) → d59, j_{12}, t_3, i_{11}
  83. Polygon(P20, H, I) → d60, i_{12}, m_4, h_{11}