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Icosidodecahedron Construction

Icosidodecahedron Construction
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2022-04-25 18:52
PolygonSolid GeometryGeometric Construction
In collections Archimedean Solids
This example demonstrates the geometric construction and properties of the icosidodecahedron, a polyhedron with faces that are both triangular and pentagonal. It involves core mathematical concepts like polygons, solid geometry, intersecting lines, and area calculations. The construction uses commands such as Polygon, Icosahedron, Sphere, Intersect, and Segment in GeoGebra. It is suitable for high school and above students to understand complex polyhedral structures and relationships.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, f, g, h, C
  2. Icosahedron(A, B, C) → a, D, faceABC, faceACF, faceAFG, faceADG, faceABD, faceBDH, faceBEH, faceBCE, faceCEI, faceCFI, E, faceEHK, faceEIK, faceIKL, faceFIL, faceHJK, faceJKL, faceGJL, faceFGL, faceDHJ, faceDGJ, F, edgeAC, edgeAB, edgeBC, edgeAF, edgeCF, edgeAG, edgeFG, edgeAD, edgeDG, edgeBD, G, edgeBH, edgeDH, edgeBE, edgeEH, edgeCE, edgeCI, edgeEI, edgeFI, edgeEK, edgeHK, H, edgeIK, edgeIL, edgeKL, edgeFL, edgeJK, edgeHJ, edgeJL, edgeGL, edgeGJ, edgeDJ, I, J, K, L
  3. Sphere(J, m) → b
  4. Intersect(edgeJK, b, 1) → M
  5. Intersect(edgeJL, b, 1) → N
  6. Intersect(edgeHJ, b, 1) → O
  7. Intersect(edgeGJ, b, 1) → P
  8. Intersect(edgeDJ, b, 1) → Q
  9. Sphere(K, m) → c
  10. Intersect(edgeKL, c) → R, I_2
  11. Intersect(edgeIK, c) → S, J_2
  12. Intersect(edgeJK, c) → T, K_2
  13. Intersect(edgeHK, c) → U, L_2
  14. Intersect(edgeEK, c) → V, M_2
  15. Sphere(I, m) → d
  16. Intersect(edgeIL, d) → W, N_2
  17. Intersect(edgeIK, d) → Z, O_2
  18. Intersect(edgeFI, d) → A_1, P_2
  19. Intersect(edgeCI, d) → B_1, Q_2
  20. Intersect(edgeEI, d) → C_1, R_2
  21. Sphere(F, m) → e
  22. Intersect(edgeFG, e) → D_1, S_2
  23. Intersect(edgeAF, e) → E_1, T_2
  24. Intersect(edgeFI, e, 1) → F_1
  25. Intersect(edgeFL, e, 1) → G_1
  26. Intersect(edgeCF, e, 1) → H_1
  27. Sphere(G, m) → i
  28. Intersect(edgeGJ, i, 1) → I_1
  29. Intersect(edgeAG, i, 1) → J_1
  30. Intersect(edgeDG, i, 1) → K_1
  31. Intersect(edgeFG, i, 1) → L_1
  32. Intersect(edgeGL, i, 1) → M_1
  33. Sphere(L, m) → j
  34. Intersect(edgeIL, j, 1) → N_1
  35. Intersect(edgeKL, j, 1) → O_1
  36. Intersect(edgeJL, j, 1) → P_1
  37. Intersect(edgeGL, j, 1) → Q_1
  38. Intersect(edgeFL, j, 1) → R_1
  39. Sphere(E, m) → k
  40. Intersect(edgeEK, k, 1) → S_1
  41. Intersect(edgeEH, k, 1) → T_1
  42. Intersect(edgeBE, k, 1) → U_1
  43. Intersect(edgeEI, k, 1) → V_1
  44. Intersect(edgeCE, k, 1) → W_1
  45. Sphere(D, m) → l
  46. Intersect(edgeDG, l) → Z_1, U_2
  47. Intersect(edgeAD, l) → A_2, V_2
  48. Intersect(edgeBD, l) → B_2, W_2
  49. Intersect(edgeDH, l) → C_2, Z_2
  50. Intersect(edgeDJ, l) → D_2, A_3
  51. Sphere(A, m) → n
  52. Intersect(edgeAD, n, 1) → E_2
  53. Intersect(edgeAG, n, 1) → F_2
  54. Intersect(edgeAF, n, 1) → G_2
  55. Sphere(B, m) → o
  56. Intersect(edgeBH, o, 1) → H_2
  57. Sphere(H, m) → p
  58. Intersect(edgeHJ, p, 1) → B_3
  59. Intersect(edgeDH, p, 1) → C_3
  60. Intersect(edgeBH, p, 1) → D_3
  61. Intersect(edgeHK, p, 1) → E_3
  62. Intersect(edgeEH, p, 1) → F_3
  63. Polygon(C_3, D_3, F_3, E_3, B_3) → poly2, c_3, d_3, f_3, e_3, b_3
  64. Polygon(U_1, W_1, V_1, S_1, T_1) → poly3, u_1, w_1, v_1, s_1, t_1
  65. Polygon(C_1, B_1, A_1, W, Z) → poly4, c_1, b_1, a_1, w, z_1
  66. Polygon(P, Q, O, M, N) → poly5, p_1, q, o_1, m_1, n_1
  67. Segment(L, G) → s
  68. Polygon(T, U, V, S, R) → poly6, t, u, v, s_2, r_1
  69. Intersect(edgeBD, o, 1) → G_3
  70. Intersect(edgeBE, o, 1) → H_3
  71. Intersect(s, j, 1) → I_3
  72. Polygon(N_1, R_1, I_3, P_1, O_1) → poly7, f_1, g_1, i_3, h_1, i_1
  73. Intersect(edgeFG, i, 1) → J_3
  74. Intersect(s, i) → K_3, P_3
  75. Polygon(J_3, J_1, K_1, I_1, K_3) → poly8, j_3, j_1, k_1, l_1, k_3
  76. Polygon(Z_1, A_2, B_2, C_2, D_2) → poly9, q_1, a_2, b_2, c_2, d_2
  77. Intersect(edgeBC, o) → L_3, Q_3
  78. Intersect(edgeAB, o) → M_3, R_3
  79. Polygon(M_3, L_3, H_3, H_2, G_3) → poly10, m_3, l_3, h_3, h_2, g_3
  80. Polygon(F_1, H_1, E_1, D_1, G_1) → poly11, d_1, e_1, f_2, g_2, i_2
  81. Intersect(edgeAC, n) → N_3, S_3
  82. Intersect(edgeAB, n) → O_3, T_3
  83. Polygon(N_3, O_3, E_2, F_2, G_2) → poly12, n_3, o_3, e_2, j_2, k_2
  84. Sphere(C, m) → l_2
  85. Intersect(edgeCF, l_2, 1) → U_3
  86. Intersect(edgeCE, l_2, 1) → V_3
  87. Intersect(edgeBC, l_2, 1) → W_3
  88. Intersect(edgeAC, l_2, 1) → Z_3
  89. Intersect(edgeCI, l_2, 1) → A_4
  90. Polygon(W_3, V_3, A_4, U_3, Z_3) → poly13, w_3, v_3, a_4, u_3, z_3
  91. Polygon(M, T, R, O_1, P_1, N) → poly14, m_2, t_2, r_2, n_2, p_2, n_4
  92. Polygon(O, B_3, E_3, U, T, M) → poly15, o_2, q_2, p_3, u_2, t_3, m_4
  93. Polygon(E_3, F_3, T_1, S_1, V, U) → poly16, q_3, r_3, s_3, a_3, v_2, u_4
  94. Polygon(V, S_1, V_1, C_1, Z, S) → poly17, v_4, f_4, g_4, h_4, z_2, s_4
  95. Polygon(R, O_1, N_1, W, Z, S) → poly18, r_4, i_4, j_4, w_2, z_4, s_5
  96. Polygon(V_1, W_1, V_3, A_4, B_1, C_1) → poly19, k_4, l_4, p_4, q_4, t_4, b_4
  97. Polygon(B_1, A_4, U_3, H_1, F_1, A_1) → poly20, c_4, d_4, e_4, f_5, g_5, h_5
  98. Polygon(W, A_1, F_1, G_1, R_1, N_1) → poly21, w_4, i_5, j_5, k_5, l_5, m_5
  99. Polygon(R_1, G_1, D_1, J_3, K_3, I_3) → poly22, n_5, p_5, q_5, r_5, t_5, a_5
  100. Polygon(P_1, I_3, K_3, I_1, P, N) → poly23, b_5, c_5, d_5, e_5, p_6, n_6
  101. Polygon(P, I_1, K_1, Z_1, D_2, Q) → poly24, p_7, f_6, g_6, h_6, i_6, q_6
  102. Polygon(Q, D_2, C_2, C_3, B_3, O) → poly25, q_7, j_6, k_6, l_6, m_6, o_4
  103. Polygon(C_2, B_2, G_3, H_2, D_3, C_3) → poly26, r_6, s_6, t_6, a_6, b_6, c_6
  104. Polygon(D_3, F_3, T_1, U_1, H_3, H_2) → poly27, d_6, e_6, f_7, g_7, h_7, i_7
  105. Polygon(V_3, W_1, U_1, H_3, L_3, W_3) → poly28, j_7, k_7, l_7, m_7, n_7, r_7
  106. Polygon(Z_3, N_3, O_3, M_3, L_3, W_3) → poly29, s_7, t_7, a_7, b_7, c_7, d_7
  107. Polygon(H_1, U_3, Z_3, N_3, G_2, E_1) → poly30, e_7, f_8, g_8, h_8, i_8, j_8
  108. Polygon(J_3, J_1, F_2, G_2, E_1, D_1) → poly31, k_8, l_8, m_8, n_8, p_8, q_8
  109. Polygon(J_1, F_2, E_2, A_2, Z_1, K_1) → poly32, r_8, s_8, t_8, a_8, b_8, c_8
  110. Polygon(E_2, O_3, M_3, G_3, B_2, A_2) → poly33, d_8, e_8, f_9, g_9, h_9, i_9

AI Drawing Prompt Reference

Draw an icosidodecahedron by first drawing triangle ABC, then constructing a dodecahedron with A, B, and C as vertices. Next, draw a sphere centered at J and find the intersections with edges JK, JL, HJ, GJ, and DJ to get points M, N, O, P, and Q. Then, draw a sphere centered at K and find the intersections with edges KL, IK, JK, and HK to get points R, S, T, and U. Continue this process to construct all vertices and edges of the icosidodecahedron.
The prompt above was compiled from the original drawing commands and is for reference only.