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Icosahedron Star Construction

Icosahedron Star Construction
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2018-10-25 00:55
PolygonSolid GeometryGeometric Construction
This example demonstrates how to construct a star polygon using the geometric properties of an icosahedron. Key math concepts include polygons, solid geometry, and geometric construction. GeoGebra commands and objects used are Icosahedron, Centroid, Intersect, and Polygon. Suitable for high school students and teachers for learning and teaching solid geometry and geometric constructions.

GeoGebra Commands & Parameters

  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}