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Rhombicosidodecahedron by chris cambré

Rhombicosidodecahedron by chris cambré
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2017-11-21 15:46
PolygonSolid GeometryGeometric Construction
This example demonstrates the geometric construction and properties of the rhombicosidodecahedron. Key math concepts include polyhedra, Euler characteristic, and symmetry. Construction highlights involve commands like Midpoint, Angle, Plane, OrthogonalLine, Rotate, and Polygon from GeoGebra. Suitable for high school solid geometry teaching, geometric modeling, and mathematical visualization exploration.

GeoGebra Commands & Parameters

  1. Midpoint(D1, D7) → A
  2. Angle(A, C, B) → α_1
  3. Plane(A, C, B) → a
  4. OrthogonalLine(C, a) → b
  5. Rotate(D1, α_1, b) → E1
  6. Rotate(D2, α_1, b) → E2
  7. Rotate(D3, α_1, b) → E3
  8. Rotate(D4, α_1, b) → E4
  9. Rotate(D5, α_1, b) → E5
  10. Rotate(D6, α_1, b) → E6
  11. Rotate(D7, α_1, b) → E7
  12. Rotate(D8, α_1, b) → E8
  13. Rotate(D9, α_1, b) → E9
  14. Rotate(D10, α_1, b) → E10
  15. Rotate(D11, α_1, b) → E11
  16. Rotate(D12, α_1, b) → E12
  17. Rotate(D13, α_1, b) → E13
  18. Rotate(D14, α_1, b) → E14
  19. Rotate(D15, α_1, b) → E15
  20. Rotate(D16, α_1, b) → E16
  21. Rotate(D17, α_1, b) → E17
  22. Rotate(D18, α_1, b) → E18
  23. Rotate(D19, α_1, b) → E19
  24. Rotate(D20, α_1, b) → E20
  25. Rotate(D21, α_1, b) → E21
  26. Rotate(D22, α_1, b) → E22
  27. Rotate(D23, α_1, b) → E23
  28. Rotate(D24, α_1, b) → E24
  29. Rotate(D25, α_1, b) → E25
  30. Rotate(D26, α_1, b) → E26
  31. Rotate(D27, α_1, b) → E27
  32. Rotate(D28, α_1, b) → E28
  33. Rotate(D29, α_1, b) → E29
  34. Rotate(D30, α_1, b) → E30
  35. Rotate(D31, α_1, b) → E31
  36. Rotate(D32, α_1, b) → E32
  37. Rotate(D33, α_1, b) → E33
  38. Rotate(D34, α_1, b) → E34
  39. Rotate(D35, α_1, b) → E35
  40. Rotate(D36, α_1, b) → E36
  41. Rotate(D37, α_1, b) → E37
  42. Rotate(D38, α_1, b) → E38
  43. Rotate(D39, α_1, b) → E39
  44. Rotate(D40, α_1, b) → E40
  45. Rotate(D41, α_1, b) → E41
  46. Rotate(D42, α_1, b) → E42
  47. Rotate(D43, α_1, b) → E43
  48. Rotate(D44, α_1, b) → E44
  49. Rotate(D45, α_1, b) → E45
  50. Rotate(D46, α_1, b) → E46
  51. Rotate(D47, α_1, b) → E47
  52. Rotate(D48, α_1, b) → E48
  53. Rotate(D49, α_1, b) → E49
  54. Rotate(D50, α_1, b) → E50
  55. Rotate(D51, α_1, b) → E51
  56. Rotate(D52, α_1, b) → E52
  57. Rotate(D53, α_1, b) → E53
  58. Rotate(D54, α_1, b) → E54
  59. Rotate(D55, α_1, b) → E55
  60. Rotate(D56, α_1, b) → E56
  61. Rotate(D57, α_1, b) → E57
  62. Rotate(D58, α_1, b) → E58
  63. Rotate(D59, α_1, b) → E59
  64. Rotate(D60, α_1, b) → E60
  65. Polygon(E52, E30, E6, E8, E32) → wielokąt1, e52, e30, e6, e8, e32
  66. Rotate(E56, α, Line[E6, E30]) → E56'
  67. Rotate(E38, α, Line[E6, E30]) → E38'
  68. Polygon(E56', E6, E30, E38') → wielokąt2, e56', e6_1, e30_1, e38'
  69. Rotate(E46, α, Line[E30, E52]) → E46'
  70. Rotate(E22, α, Line[E30, E52]) → E22'
  71. Polygon(E46', E30, E52, E22') → wielokąt3, e46', e30_2, e52_1, e22'
  72. Rotate(E24, α, Line[E52, E32]) → E24'
  73. Rotate(E48, α, Line[E52, E32]) → E48'
  74. Polygon(E52, E24', E48', E32) → wielokąt4, e52_2, e24', e48', e32_1
  75. Rotate(E40, α, Line[E32, E8]) → E40'
  76. Rotate(E54, α, Line[E32, E8]) → E54'
  77. Polygon(E32, E40', E54', E8) → wielokąt5, e32_2, e40', e54', e8_1
  78. Rotate(E4, α, Line[E8, E6]) → E4'
  79. Rotate(E2, α, Line[E8, E6]) → E2'
  80. Polygon(E8, E6, E2', E4') → wielokąt6, e8_2, e6_2, e2', e4'
  81. Rotate(Rotate[E56, β, Line[E2, E6]], α, Line[E8, E6]) → D
  82. Polygon(E6, D, E2') → wielokąt7, e2'_1, e6_3, d
  83. Rotate(Rotate[E46, β, Line[E38, E30]], α, Line[E6, E30]) → E
  84. Polygon(E30, E, E38') → wielokąt8, e38'_1, e30_3, e
  85. Rotate(Rotate[E24, β, Line[E22, E52]], α, Line[E30, E52]) → F
  86. Polygon(E52, F, E22') → wielokąt9, e22'_1, e52_3, f_1
  87. Rotate(Rotate[E40, β, Line[E48, E32]], α, Line[E52, E32]) → G
  88. Polygon(E32, G, E48') → wielokąt10, e48'_1, e32_3, g
  89. Rotate(Rotate[E4, β, Line[E54, E8]], α, Line[E32, E8]) → H
  90. Polygon(E8, H, E54') → wielokąt11, e54'_1, e8_3, h
  91. Rotate(Rotate[E23, α, Line[E24, E48]], α, Line[E52, E32]) → I
  92. Rotate(Rotate[E47, α, Line[E24, E48]], α, Line[E52, E32]) → J
  93. Rotate(Rotate[E60, α, Line[E24, E48]], α, Line[E52, E32]) → K
  94. Polygon(I, E24', E48', K, J) → wielokąt12, i, e24'_1, e48'_2, k, j
  95. Rotate(Rotate[E16, α, Line[E40, E54]], α, Line[E32, E8]) → L
  96. Rotate(Rotate[E12, α, Line[E40, E54]], α, Line[E32, E8]) → M
  97. Rotate(Rotate[E36, α, Line[E40, E54]], α, Line[E32, E8]) → N
  98. Polygon(E54', N, M, L, E40') → wielokąt13, e54'_2, n, m, l, e40'_1
  99. Rotate(Rotate[E28, α, Line[E4, E2]], α, Line[E8, E6]) → O
  100. Rotate(Rotate[E50, α, Line[E4, E2]], α, Line[E8, E6]) → P
  101. Rotate(Rotate[E26, α, Line[E4, E2]], α, Line[E8, E6]) → Q
  102. Polygon(E4', E2', Q, P, O) → wielokąt14, e4'_1, e2'_2, q, p, o
  103. Rotate(Rotate[E34, α, Line[E56, E38]], α, Line[E6, E30]) → R
  104. Rotate(Rotate[E10, α, Line[E56, E38]], α, Line[E6, E30]) → S
  105. Rotate(Rotate[E14, α, Line[E56, E38]], α, Line[E6, E30]) → T
  106. Polygon(R, E56', E38', T, S) → wielokąt15, r, e56'_1, e38'_2, t, s_1
  107. Rotate(Rotate[E59, α, Line[E46, E22]], α, Line[E30, E52]) → U
  108. Rotate(Rotate[E45, α, Line[E46, E22]], α, Line[E30, E52]) → V
  109. Rotate(Rotate[E21, α, Line[E46, E22]], α, Line[E30, E52]) → W
  110. Polygon(E46', U, V, W, E22') → wielokąt16, e46'_1, u, v, w, e22'_2
  111. Rotate(Rotate[Rotate[E42, α, Line[E34, E10]], α, Line[E56, E38]], α, Line[E6, E30]) → Z
  112. Rotate(Rotate[Rotate[E57, α, Line[E34, E10]], α, Line[E56, E38]], α, Line[E6, E30]) → A_1
  113. Polygon(Z, R, S, A_1) → wielokąt17, z_1, r_1, s_2, a_1
  114. Rotate(Rotate[Rotate[E9, α, Line[E10, E14]], α, Line[E56, E38]], α, Line[E6, E30]) → B_1
  115. Rotate(Rotate[Rotate[E13, α, Line[E10, E14]], α, Line[E56, E38]], α, Line[E6, E30]) → C_1
  116. Rotate(Rotate[Rotate[E59, α, Line[E14, E38]], α, Line[E56, E38]], α, Line[E6, E30]) → D_1
  117. Rotate(Rotate[Rotate[E46, α, Line[E14, E38]], α, Line[E56, E38]], α, Line[E6, E30]) → E_1
  118. Polygon(S, T, C_1, B_1) → wielokąt18, s_3, t_1, c_1, b_1
  119. Polygon(E38', E_1, D_1, T) → wielokąt19, e38'_3, e_1, d_1, t_2
  120. Rotate(Rotate[Rotate[E13, α, Line[E59, E45]], α, Line[E46, E22]], α, Line[E30, E52]) → F_1
  121. Rotate(Rotate[Rotate[E37, α, Line[E59, E45]], α, Line[E46, E22]], α, Line[E30, E52]) → G_1
  122. Rotate(Rotate[Rotate[E29, α, Line[E45, E21]], α, Line[E46, E22]], α, Line[E30, E52]) → H_1
  123. Rotate(Rotate[Rotate[E51, α, Line[E45, E21]], α, Line[E46, E22]], α, Line[E30, E52]) → I_1
  124. Rotate(Rotate[Rotate[E23, α, Line[E21, E22]], α, Line[E46, E22]], α, Line[E30, E52]) → J_1
  125. Rotate(Rotate[Rotate[E24, α, Line[E21, E22]], α, Line[E46, E22]], α, Line[E30, E52]) → K_1
  126. Polygon(U, V, G_1, F_1) → wielokąt20, u_1, v_1, g_1, f_2
  127. Polygon(V, H_1, I_1, W) → wielokąt21, v_2, h_1, i_1, w_1
  128. Polygon(E22', K_1, J_1, W) → wielokąt22, e22'_3, k_1, j_1, w_2
  129. Rotate(Rotate[Rotate[E51, α, Line[E23, E47]], α, Line[E24, E48]], α, Line[E52, E32]) → L_1
  130. Rotate(Rotate[Rotate[E31, α, Line[E23, E47]], α, Line[E24, E48]], α, Line[E52, E32]) → M_1
  131. Rotate(Rotate[Rotate[E39, α, Line[E47, E60]], α, Line[E24, E48]], α, Line[E52, E32]) → N_1
  132. Rotate(Rotate[Rotate[E15, α, Line[E47, E60]], α, Line[E24, E48]], α, Line[E52, E32]) → O_1
  133. Rotate(Rotate[Rotate[E16, α, Line[E60, E48]], α, Line[E24, E48]], α, Line[E52, E32]) → P_1
  134. Rotate(Rotate[Rotate[E40, α, Line[E60, E48]], α, Line[E24, E48]], α, Line[E52, E32]) → Q_1
  135. Polygon(L_1, I, J, M_1) → wielokąt23, l_1, i_2, j_2, m_1
  136. Polygon(J, N_1, O_1, K) → wielokąt24, j_3, n_1, o_1, k_2
  137. Polygon(E48', Q_1, P_1, K) → wielokąt25, e48'_3, q_1, p_1, k_3
  138. Rotate(Rotate[Rotate[E15, α, Line[E16, E12]], α, Line[E40, E54]], α, Line[E32, E8]) → R_1
  139. Rotate(Rotate[Rotate[E11, α, Line[E16, E12]], α, Line[E40, E54]], α, Line[E32, E8]) → S_1
  140. Rotate(Rotate[Rotate[E58, α, Line[E12, E36]], α, Line[E40, E54]], α, Line[E32, E8]) → T_1
  141. Rotate(Rotate[Rotate[E44, α, Line[E12, E36]], α, Line[E40, E54]], α, Line[E32, E8]) → U_1
  142. Rotate(Rotate[Rotate[E28, α, Line[E36, E54]], α, Line[E40, E54]], α, Line[E32, E8]) → V_1
  143. Rotate(Rotate[Rotate[E4, α, Line[E36, E54]], α, Line[E40, E54]], α, Line[E32, E8]) → W_1
  144. Polygon(L, M, S_1, R_1) → wielokąt26, l_2, m_2, s_4, r_2
  145. Polygon(M, T_1, U_1, N) → wielokąt27, m_3, t_3, u_2, n_2
  146. Polygon(E54', W_1, V_1, N) → wielokąt28, e54'_3, w_3, v_3, n_3
  147. Rotate(Rotate[Rotate[E44, α, Line[E28, E50]], α, Line[E4, E2]], α, Line[E8, E6]) → Z_1
  148. Rotate(Rotate[Rotate[E20, α, Line[E28, E50]], α, Line[E4, E2]], α, Line[E8, E6]) → A_2
  149. Rotate(Rotate[Rotate[E18, α, Line[E50, E26]], α, Line[E4, E2]], α, Line[E8, E6]) → B_2
  150. Rotate(Rotate[Rotate[E42, α, Line[E50, E26]], α, Line[E4, E2]], α, Line[E8, E6]) → C_2
  151. Rotate(Rotate[Rotate[E34, α, Line[E26, E2]], α, Line[E4, E2]], α, Line[E8, E6]) → D_2
  152. Rotate(Rotate[Rotate[E56, α, Line[E26, E2]], α, Line[E4, E2]], α, Line[E8, E6]) → E_2
  153. Polygon(E2', E_2, D_2, Q) → wielokąt29, e2'_3, e_2, d_2, q_2
  154. Polygon(Q, C_2, B_2, P) → wielokąt30, q_3, c_2, b_2, p_2
  155. Polygon(P, A_2, Z_1, O) → wielokąt31, p_3, a_2, z_2, o_2
  156. Rotate(Rotate[Rotate[Rotate[E44, β, Line[E36, E28]], α, Line[E36, E54]], α, Line[E40, E54]], α, Line[E32, E8]) → F_2
  157. Polygon(N, F_2, V_1) → wielokąt32, v_4, n_4, f_3
  158. Rotate(Rotate[Rotate[Rotate[E42, β, Line[E26, E34]], α, Line[E26, E2]], α, Line[E4, E2]], α, Line[E8, E6]) → G_2
  159. Polygon(Q, G_2, D_2) → wielokąt33, d_3, q_4, g_2
  160. Rotate(Rotate[Rotate[Rotate[E13, β, Line[E14, E59]], α, Line[E14, E38]], α, Line[E56, E38]], α, Line[E6, E30]) → H_2
  161. Polygon(T, H_2, D_1) → wielokąt34, d_4, t_4, h_2
  162. Rotate(Rotate[Rotate[Rotate[E51, β, Line[E21, E23]], α, Line[E21, E22]], α, Line[E46, E22]], α, Line[E30, E52]) → I_2
  163. Polygon(W, I_2, J_1) → wielokąt35, j_4, w_4, i_3
  164. Rotate(Rotate[Rotate[Rotate[E15, β, Line[E60, E16]], α, Line[E60, E48]], α, Line[E24, E48]], α, Line[E52, E32]) → J_2
  165. Polygon(K, J_2, P_1) → wielokąt36, p_4, k_4, j_5
  166. Rotate(Rotate[Rotate[Rotate[E39, β, Line[E31, E47]], α, Line[E23, E47]], α, Line[E24, E48]], α, Line[E52, E32]) → K_2
  167. Polygon(J, K_2, M_1) → wielokąt37, m_4, j_6, k_5
  168. Rotate(Rotate[Rotate[Rotate[E58, β, Line[E11, E12]], α, Line[E16, E12]], α, Line[E40, E54]], α, Line[E32, E8]) → L_2
  169. Polygon(M, L_2, S_1) → wielokąt38, s_5, m_5, l_3
  170. Rotate(Rotate[Rotate[Rotate[E18, β, Line[E20, E50]], α, Line[E28, E50]], α, Line[E4, E2]], α, Line[E8, E6]) → M_2
  171. Polygon(P, M_2, A_2) → wielokąt39, a_3, p_5, m_6
  172. Rotate(Rotate[Rotate[Rotate[E9, β, Line[E57, E10]], α, Line[E34, E10]], α, Line[E56, E38]], α, Line[E6, E30]) → N_2
  173. Polygon(S, N_2, A_1) → wielokąt40, a_4, s_6, n_5
  174. Rotate(Rotate[Rotate[Rotate[E29, β, Line[E37, E45]], α, Line[E59, E45]], α, Line[E46, E22]], α, Line[E30, E52]) → O_2
  175. Polygon(V, O_2, G_1) → wielokąt41, g_3, v_5, o_3
  176. Rotate(Rotate[Rotate[Rotate[E33, α, Line[E9, E13]], α, Line[E10, E14]], α, Line[E56, E38]], α, Line[E6, E30]) → P_2
  177. Rotate(Rotate[Rotate[Rotate[E53, α, Line[E9, E13]], α, Line[E10, E14]], α, Line[E56, E38]], α, Line[E6, E30]) → Q_2
  178. Rotate(Rotate[Rotate[Rotate[E37, α, Line[E9, E13]], α, Line[E10, E14]], α, Line[E56, E38]], α, Line[E6, E30]) → R_2
  179. Polygon(C_1, R_2, Q_2, P_2, B_1) → wielokąt42, c_3, r_3, q_5, p_6, b_3
  180. Rotate(Rotate[Rotate[Rotate[E5, α, Line[E29, E51]], α, Line[E45, E21]], α, Line[E46, E22]], α, Line[E30, E52]) → S_2
  181. Rotate(Rotate[Rotate[Rotate[E7, α, Line[E29, E51]], α, Line[E45, E21]], α, Line[E46, E22]], α, Line[E30, E52]) → T_2
  182. Rotate(Rotate[Rotate[Rotate[E31, α, Line[E29, E51]], α, Line[E45, E21]], α, Line[E46, E22]], α, Line[E30, E52]) → U_2
  183. Polygon(H_1, I_1, U_2, T_2, S_2) → wielokąt43, h_3, i_4, u_3, t_5, s_7
  184. Rotate(Rotate[Rotate[Rotate[E55, α, Line[E39, E15]], α, Line[E47, E60]], α, Line[E24, E48]], α, Line[E52, E32]) → V_2
  185. Rotate(Rotate[Rotate[Rotate[E35, α, Line[E39, E15]], α, Line[E47, E60]], α, Line[E24, E48]], α, Line[E52, E32]) → W_2
  186. Rotate(Rotate[Rotate[Rotate[E11, α, Line[E39, E15]], α, Line[E47, E60]], α, Line[E24, E48]], α, Line[E52, E32]) → Z_2
  187. Polygon(V_2, N_1, O_1, Z_2, W_2) → wielokąt44, v_6, n_6, o_4, z_3, w_5
  188. Rotate(Rotate[Rotate[Rotate[E43, α, Line[E58, E44]], α, Line[E12, E36]], α, Line[E40, E54]], α, Line[E32, E8]) → A_3
  189. Rotate(Rotate[Rotate[Rotate[E19, α, Line[E58, E44]], α, Line[E12, E36]], α, Line[E40, E54]], α, Line[E32, E8]) → B_3
  190. Rotate(Rotate[Rotate[Rotate[E20, α, Line[E58, E44]], α, Line[E12, E36]], α, Line[E40, E54]], α, Line[E32, E8]) → C_3
  191. Polygon(T_1, U_1, C_3, B_3, A_3) → wielokąt45, t_6, u_4, c_4, b_4, a_5
  192. Rotate(Rotate[Rotate[Rotate[E17, α, Line[E18, E42]], α, Line[E50, E26]], α, Line[E4, E2]], α, Line[E8, E6]) → D_3
  193. Rotate(Rotate[Rotate[Rotate[E41, α, Line[E18, E42]], α, Line[E50, E26]], α, Line[E4, E2]], α, Line[E8, E6]) → E_3
  194. Rotate(Rotate[Rotate[Rotate[E57, α, Line[E18, E42]], α, Line[E50, E26]], α, Line[E4, E2]], α, Line[E8, E6]) → F_3
  195. Polygon(C_2, F_3, E_3, D_3, B_2) → wielokąt46, c_5, f_4, e_3, d_5, b_5
  196. Rotate(Rotate[Rotate[Rotate[Rotate[E17, α, Line[E19, E20]], α, Line[E58, E44]], α, Line[E12, E36]], α, Line[E40, E54]], α, Line[E32, E8]) → G_3
  197. Rotate(Rotate[Rotate[Rotate[Rotate[E18, α, Line[E19, E20]], α, Line[E58, E44]], α, Line[E12, E36]], α, Line[E40, E54]], α, Line[E32, E8]) → H_3
  198. Polygon(B_3, C_3, H_3, G_3) → wielokąt47, b_6, c_6, h_4, g_4
  199. Rotate(Rotate[Rotate[Rotate[Rotate[E33, α, Line[E41, E57]], α, Line[E18, E42]], α, Line[E50, E26]], α, Line[E4, E2]], α, Line[E8, E6]) → I_3
  200. Rotate(Rotate[Rotate[Rotate[Rotate[E9, α, Line[E41, E57]], α, Line[E18, E42]], α, Line[E50, E26]], α, Line[E4, E2]], α, Line[E8, E6]) → J_3
  201. Polygon(E_3, I_3, J_3, F_3) → wielokąt48, e_4, i_5, j_7, f_5
  202. Rotate(Rotate[Rotate[Rotate[Rotate[E5, α, Line[E53, E37]], α, Line[E9, E13]], α, Line[E10, E14]], α, Line[E56, E38]], α, Line[E6, E30]) → K_3
  203. Rotate(Rotate[Rotate[Rotate[Rotate[E29, α, Line[E53, E37]], α, Line[E9, E13]], α, Line[E10, E14]], α, Line[E56, E38]], α, Line[E6, E30]) → L_3
  204. Polygon(Q_2, K_3, L_3, R_2) → wielokąt49, q_6, k_6, l_4, r_4
  205. Rotate(Rotate[Rotate[Rotate[Rotate[E55, α, Line[E7, E31]], α, Line[E29, E51]], α, Line[E45, E21]], α, Line[E46, E22]], α, Line[E30, E52]) → M_3
  206. Rotate(Rotate[Rotate[Rotate[Rotate[E39, α, Line[E7, E31]], α, Line[E29, E51]], α, Line[E45, E21]], α, Line[E46, E22]], α, Line[E30, E52]) → N_3
  207. Polygon(T_2, M_3, N_3, U_2) → wielokąt50, t_7, m_7, n_7, u_5
  208. Rotate(Rotate[Rotate[Rotate[Rotate[E43, α, Line[E35, E11]], α, Line[E39, E15]], α, Line[E47, E60]], α, Line[E24, E48]], α, Line[E52, E32]) → O_3
  209. Rotate(Rotate[Rotate[Rotate[Rotate[E58, α, Line[E35, E11]], α, Line[E39, E15]], α, Line[E47, E60]], α, Line[E24, E48]], α, Line[E52, E32]) → P_3
  210. Polygon(W_2, Z_2, P_3, O_3) → wielokąt51, w_6, z_4, p_7, o_5
  211. Rotate(Rotate[Rotate[Rotate[Rotate[E27, α, Line[E55, E35]], α, Line[E39, E15]], α, Line[E47, E60]], α, Line[E24, E48]], α, Line[E52, E32]) → Q_3
  212. Rotate(Rotate[Rotate[Rotate[Rotate[E3, α, Line[E55, E35]], α, Line[E39, E15]], α, Line[E47, E60]], α, Line[E24, E48]], α, Line[E52, E32]) → R_3
  213. Polygon(R_3, Q_3, W_2, V_2) → wielokąt52, r_5, q_7, w_7, v_7
  214. Rotate(Rotate[Rotate[Rotate[Rotate[E27, α, Line[E43, E19]], α, Line[E58, E44]], α, Line[E12, E36]], α, Line[E40, E54]], α, Line[E32, E8]) → S_3
  215. Rotate(Rotate[Rotate[Rotate[Rotate[E49, α, Line[E43, E19]], α, Line[E58, E44]], α, Line[E12, E36]], α, Line[E40, E54]], α, Line[E32, E8]) → T_3
  216. Polygon(S_3, A_3, B_3, T_3) → wielokąt53, s_8, a_6, b_7, t_8
  217. Rotate(Rotate[Rotate[Rotate[Rotate[E49, α, Line[E17, E41]], α, Line[E18, E42]], α, Line[E50, E26]], α, Line[E4, E2]], α, Line[E8, E6]) → U_3
  218. Rotate(Rotate[Rotate[Rotate[Rotate[E25, α, Line[E17, E41]], α, Line[E18, E42]], α, Line[E50, E26]], α, Line[E4, E2]], α, Line[E8, E6]) → V_3
  219. Polygon(U_3, V_3, E_3, D_3) → wielokąt54, u_6, v_8, e_5, d_6
  220. Rotate(Rotate[Rotate[Rotate[Rotate[E25, α, Line[E33, E53]], α, Line[E9, E13]], α, Line[E10, E14]], α, Line[E56, E38]], α, Line[E6, E30]) → W_3
  221. Rotate(Rotate[Rotate[Rotate[Rotate[E1, α, Line[E33, E53]], α, Line[E9, E13]], α, Line[E10, E14]], α, Line[E56, E38]], α, Line[E6, E30]) → Z_3
  222. Polygon(W_3, P_2, Q_2, Z_3) → wielokąt55, w_8, p_8, q_8, z_5
  223. Rotate(Rotate[Rotate[Rotate[Rotate[E1, α, Line[E5, E7]], α, Line[E29, E51]], α, Line[E45, E21]], α, Line[E46, E22]], α, Line[E30, E52]) → A_4
  224. Rotate(Rotate[Rotate[Rotate[Rotate[E3, α, Line[E5, E7]], α, Line[E29, E51]], α, Line[E45, E21]], α, Line[E46, E22]], α, Line[E30, E52]) → B_4
  225. Polygon(A_4, S_2, T_2, B_4) → wielokąt56, a_7, s_9, t_9, b_8
  226. Rotate(Rotate[Rotate[Rotate[Rotate[Rotate[E25, α, Line[E1, E3]], α, Line[E5, E7]], α, Line[E29, E51]], α, Line[E45, E21]], α, Line[E46, E22]], α, Line[E30, E52]) → C_4
  227. Rotate(Rotate[Rotate[Rotate[Rotate[Rotate[E49, α, Line[E1, E3]], α, Line[E5, E7]], α, Line[E29, E51]], α, Line[E45, E21]], α, Line[E46, E22]], α, Line[E30, E52]) → D_4
  228. Rotate(Rotate[Rotate[Rotate[Rotate[Rotate[E27, α, Line[E1, E3]], α, Line[E5, E7]], α, Line[E29, E51]], α, Line[E45, E21]], α, Line[E46, E22]], α, Line[E30, E52]) → E_4
  229. Polygon(C_4, A_4, B_4, E_4, D_4) → wielokąt57, c_7, a_8, b_9, e_6, d_7
  230. Rotate(Rotate[Rotate[Rotate[Rotate[Rotate[E7, β, Line[E55, E3]], α, Line[E55, E35]], α, Line[E39, E15]], α, Line[E47, E60]], α, Line[E24, E48]], α, Line[E52, E32]) → F_4
  231. Polygon(R_3, F_4, V_2) → wielokąt58, v_9, r_6, f_6
  232. Rotate(Rotate[Rotate[Rotate[Rotate[Rotate[E35, β, Line[E43, E27]], α, Line[E43, E19]], α, Line[E58, E44]], α, Line[E12, E36]], α, Line[E40, E54]], α, Line[E32, E8]) → G_4
  233. Polygon(S_3, G_4, A_3) → wielokąt59, a_9, s_{10}, g_5
  234. Rotate(Rotate[Rotate[Rotate[Rotate[Rotate[E19, β, Line[E17, E49]], α, Line[E17, E41]], α, Line[E18, E42]], α, Line[E50, E26]], α, Line[E4, E2]], α, Line[E8, E6]) → H_4
  235. Polygon(U_3, H_4, D_3) → wielokąt60, d_8, u_7, h_5
  236. Rotate(Rotate[Rotate[Rotate[Rotate[Rotate[E41, β, Line[E33, E25]], α, Line[E33, E53]], α, Line[E9, E13]], α, Line[E10, E14]], α, Line[E56, E38]], α, Line[E6, E30]) → I_4
  237. Polygon(W_3, I_4, P_2) → wielokąt61, p_9, w_9, i_6
  238. Rotate(Rotate[Rotate[Rotate[Rotate[E53, β, Line[E5, E1]], α, Line[E29, E51]], α, Line[E45, E21]], α, Line[E46, E22]], α, Line[E30, E52]) → J_4
  239. Polygon(A_4, J_4, S_2) → wielokąt62, s_{11}, a_{10}, j_8

AI Drawing Prompt Reference

Draw a rhombicosidodecahedron by first finding the midpoint A of D1 and D7, then calculating the angle α1 between A, C, and B, and rotating D1 around α1 in plane b to get E1. Repeat this process for D2 to D44, resulting in all vertices of the rhombicosidodecahedron.
The prompt above was compiled from the original drawing commands and is for reference only.