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截半二十面体 by chris cambré (2)

截半二十面体 by chris cambré (2)
几何画板及绘图内容加载中，请稍等……
2017-11-21 15:46
多边形立体几何几何作图
①本范例演示了截半二十面体的几何构造与性质；②涉及的核心数学概念包括多面体、欧拉示性数、对称性；③作图要点——从下方『构造摘要』提炼用到了哪些 GeoGebra 命令/对象：Midpoint（中点）、Angle（角度）、Plane（平面）、OrthogonalLine（垂线）、Rotate（旋转）、Polygon（多边形）；④适合的学段或用途：高中立体几何教学、几何建模、数学可视化探索。

GeoGebra 命令及参数

  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 绘图提示语参考

绘制一个菱形三十面体，首先找到点D1和D7的中点A，然后计算角ABC的大小α1，接着以点C为原点，α1为角度，b为平面的法线方向，旋转点D1至E1，重复此过程，依次旋转D2至D44，最终得到菱形三十面体的所有顶点。
以上提示语为根据原始绘图命令整理而来，仅供参考。