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Geometric Construction of Escher-Style Butterflies

Geometric Construction of Escher-Style Butterflies
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2023-03-22 23:19
VectorCoordinate GeometryProbability & StatisticsTransformationGeometric Construction
In collections geometriadinamica.es
This example demonstrates how to use GeoGebra to create Escher-style butterfly patterns. Key mathematical concepts include geometric transformations, symmetry, and rotation. Using commands such as If, Line, Rotate, Point, Intersect, Polygon, Mirror, Vector, Translate, Angle, Midpoint, Min, the user can construct beautiful geometric patterns. Suitable for high school math education and enthusiasts.

GeoGebra Commands & Parameters

  1. If(a < 1, a, 1) → d1
  2. If(a < 1.2, 0, If[a < 2.2, a - 1.2, 1]) → d2
  3. If(a < 2.3, 0, If[a < 3.3, a - 2.3, 1]) → d3
  4. Line(C, D) → b
  5. Rotate(b, 59.99999999999999°, C) → b'
  6. Point(b) → E
  7. Rotate(b, 119.99999999999999°, E) → b'_1
  8. Intersect(b', b'_1) → F
  9. Polygon(F, E, O, P, Q, R, S, T, U, V, W, Z, G, H, I, J, K, L, M, N) → poly1, f, n, o, p, q, r, s, t, u, v_1, w, e, z, g, h, i, j, k, l, m
  10. Point(b) → A_1
  11. Rotate(N, ((-d1) * 300°), F) → N'
  12. Rotate(A_1, ((-d1) * 300°), F) → B_1
  13. Rotate(C, ((-d1) * 300°), F) → C'
  14. Rotate(F, ((-d1) * 300°), F) → F'
  15. Rotate(Z, ((-d1) * 300°), F) → Z'
  16. Rotate(W, ((-d1) * 300°), F) → W'
  17. Rotate(V, ((-d1) * 300°), F) → V'
  18. Rotate(U, ((-d1) * 300°), F) → U'
  19. Rotate(T, ((-d1) * 300°), F) → T'
  20. Rotate(S, ((-d1) * 300°), F) → S'
  21. Rotate(R, ((-d1) * 300°), F) → R'
  22. Rotate(Q, ((-d1) * 300°), F) → Q'
  23. Rotate(P, ((-d1) * 300°), F) → P'
  24. Rotate(O, ((-d1) * 300°), F) → O'
  25. Polygon(N', B_1, R', Q', P', O', C', F', Z', W', V', U', T', S') → poly2', n', s', r', q', p', o', b_1, c', f', z', w', v', u', t'
  26. Rotate(E, (d1 * 240°), E) → E'
  27. Rotate(A_1, (d1 * 240°), E) → C_1
  28. Rotate(N, (d1 * 240°), E) → N'_1
  29. Rotate(M, (d1 * 240°), E) → M'
  30. Rotate(L, (d1 * 240°), E) → L'
  31. Rotate(K, (d1 * 240°), E) → K'
  32. Rotate(J, (d1 * 240°), E) → J'
  33. Rotate(I, (d1 * 240°), E) → I'
  34. Rotate(H, (d1 * 240°), E) → H'
  35. Rotate(G, (d1 * 240°), E) → G'
  36. Polygon(E', C_1, N'_1, M', L', K', J', I', H', G') → poly3', e', g', c_2, n'_1, m', l', k', j', i', h'
  37. If(a < 3.4, 0, If[a < 4.4, a - 3.4, 1]) → d4
  38. If(a < 4.5, 0, If[a < 5.5, a - 4.5, 1]) → d5
  39. If(a < 5.6, 0, If[a < 6.6, a - 5.6, 1]) → d6
  40. If(a < 6.7, 0, If[a < 7.7, a - 6.7, 1]) → d7
  41. If(a < 7.8, 0, If[a < 8.8, a - 7.8, 1]) → d8
  42. Rotate(F, (d2 * 60°), F) → F'_1
  43. Rotate(E, (d2 * 60°), F) → E'_1
  44. Rotate(G, (d2 * 60°), F) → G'_1
  45. Rotate(H, (d2 * 60°), F) → H'_1
  46. Rotate(I, (d2 * 60°), F) → I'_1
  47. Rotate(J, (d2 * 60°), F) → J'_1
  48. Rotate(K, (d2 * 60°), F) → K'_1
  49. Rotate(L, (d2 * 60°), F) → L'_1
  50. Rotate(M, (d2 * 60°), F) → M'_1
  51. Rotate(N, (d2 * 60°), F) → N'_2
  52. Rotate(O, (d2 * 60°), F) → O'_1
  53. Rotate(P, (d2 * 60°), F) → P'_1
  54. Rotate(Q, (d2 * 60°), F) → Q'_1
  55. Rotate(R, (d2 * 60°), F) → R'_1
  56. Rotate(S, (d2 * 60°), F) → S'_1
  57. Rotate(T, (d2 * 60°), F) → T'_1
  58. Rotate(U, (d2 * 60°), F) → U'_1
  59. Rotate(V, (d2 * 60°), F) → V'_1
  60. Rotate(W, (d2 * 60°), F) → W'_1
  61. Rotate(Z, (d2 * 60°), F) → Z'_1
  62. Polygon(F'_1, E'_1, O'_1, P'_1, Q'_1, R'_1, S'_1, T'_1, U'_1, V'_1, W'_1, Z'_1, G'_1, H'_1, I'_1, J'_1, K'_1, L'_1, M'_1, N'_2) → poly1', f'_1, n'_2, o'_1, p'_1, q'_1, r'_1, s'_1, t'_1, u'_1, v'_1, w'_1, e'_1, z'_1, g'_1, h'_1, i'_1, j'_1, k'_1, l'_1, m'_1
  63. Rotate(N', (d2 * 60°), F) → N''
  64. Rotate(B_1, (d2 * 60°), F) → D_1
  65. Rotate(C', (d2 * 60°), F) → C''
  66. Rotate(F', (d2 * 60°), F) → F''
  67. Rotate(Z', (d2 * 60°), F) → Z''
  68. Rotate(W', (d2 * 60°), F) → W''
  69. Rotate(V', (d2 * 60°), F) → V''
  70. Rotate(U', (d2 * 60°), F) → U''
  71. Rotate(T', (d2 * 60°), F) → T''
  72. Rotate(S', (d2 * 60°), F) → S''
  73. Rotate(R', (d2 * 60°), F) → R''
  74. Rotate(Q', (d2 * 60°), F) → Q''
  75. Rotate(P', (d2 * 60°), F) → P''
  76. Rotate(O', (d2 * 60°), F) → O''
  77. Polygon(N'', D_1, R'', Q'', P'', O'', C'', F'', Z'', W'', V'', U'', T'', S'') → poly2'', n'', s'', r'', q'', p'', o'', d_1, c'', f'', z'', w'', v'', u'', t''
  78. Rotate(E', (d2 * 60°), F) → E''
  79. Rotate(C_1, (d2 * 60°), F) → E_1
  80. Rotate(N'_1, (d2 * 60°), F) → F_1
  81. Rotate(M', (d2 * 60°), F) → M''
  82. Rotate(L', (d2 * 60°), F) → L''
  83. Rotate(K', (d2 * 60°), F) → K''
  84. Rotate(J', (d2 * 60°), F) → J''
  85. Rotate(I', (d2 * 60°), F) → I''
  86. Rotate(H', (d2 * 60°), F) → H''
  87. Rotate(G', (d2 * 60°), F) → G''
  88. Polygon(E'', E_1, F_1, M'', L'', K'', J'', I'', H'', G'') → poly3'', e'', g'', e_1, f_1, m'', l'', k'', j'', i'', h''
  89. Rotate(F'_1, (d3 * 60°), F) → G_1
  90. Rotate(E'_1, (d3 * 60°), F) → H_1
  91. Rotate(G'_1, (d3 * 60°), F) → I_1
  92. Rotate(H'_1, (d3 * 60°), F) → J_1
  93. Rotate(I'_1, (d3 * 60°), F) → K_1
  94. Rotate(J'_1, (d3 * 60°), F) → L_1
  95. Rotate(K'_1, (d3 * 60°), F) → M_1
  96. Rotate(L'_1, (d3 * 60°), F) → N_1
  97. Rotate(M'_1, (d3 * 60°), F) → O_1
  98. Rotate(N'_2, (d3 * 60°), F) → P_1
  99. Rotate(O'_1, (d3 * 60°), F) → Q_1
  100. Rotate(P'_1, (d3 * 60°), F) → R_1
  101. Rotate(Q'_1, (d3 * 60°), F) → S_1
  102. Rotate(R'_1, (d3 * 60°), F) → T_1
  103. Rotate(S'_1, (d3 * 60°), F) → U_1
  104. Rotate(T'_1, (d3 * 60°), F) → V_1
  105. Rotate(U'_1, (d3 * 60°), F) → W_1
  106. Rotate(V'_1, (d3 * 60°), F) → Z_1
  107. Rotate(W'_1, (d3 * 60°), F) → A_2
  108. Rotate(Z'_1, (d3 * 60°), F) → B_2
  109. Polygon(G_1, H_1, Q_1, R_1, S_1, T_1, U_1, V_1, W_1, Z_1, A_2, B_2, I_1, J_1, K_1, L_1, M_1, N_1, O_1, P_1) → poly1'', g_1, p_1, q_1, r_1, s_1, t_1, u_1, v_2, w_1, z_1, a_2, h_1, b_2, i_1, j_1, k_1, l_1, m_1, n_1, o_1
  110. Rotate(N'', (d3 * 60°), F) → N'''
  111. Rotate(D_1, (d3 * 60°), F) → C_2
  112. Rotate(C'', (d3 * 60°), F) → C'''
  113. Rotate(F'', (d3 * 60°), F) → F'''
  114. Rotate(Z'', (d3 * 60°), F) → Z'''
  115. Rotate(W'', (d3 * 60°), F) → W'''
  116. Rotate(V'', (d3 * 60°), F) → V'''
  117. Rotate(U'', (d3 * 60°), F) → U'''
  118. Rotate(T'', (d3 * 60°), F) → T'''
  119. Rotate(S'', (d3 * 60°), F) → S'''
  120. Rotate(R'', (d3 * 60°), F) → R'''
  121. Rotate(Q'', (d3 * 60°), F) → Q'''
  122. Rotate(P'', (d3 * 60°), F) → P'''
  123. Rotate(O'', (d3 * 60°), F) → O'''
  124. Polygon(N''', C_2, R''', Q''', P''', O''', C''', F''', Z''', W''', V''', U''', T''', S''') → poly2''', n''', s''', r''', q''', p''', o''', c_1, c''', f''', z''', w''', v''', u''', t'''
  125. Rotate(E'', (d3 * 60°), F) → E'''
  126. Rotate(E_1, (d3 * 60°), F) → D_2
  127. Rotate(F_1, (d3 * 60°), F) → E_2
  128. Rotate(M'', (d3 * 60°), F) → M'''
  129. Rotate(L'', (d3 * 60°), F) → L'''
  130. Rotate(K'', (d3 * 60°), F) → K'''
  131. Rotate(J'', (d3 * 60°), F) → J'''
  132. Rotate(I'', (d3 * 60°), F) → I'''
  133. Rotate(H'', (d3 * 60°), F) → H'''
  134. Rotate(G'', (d3 * 60°), F) → G'''
  135. Polygon(E''', D_2, E_2, M''', L''', K''', J''', I''', H''', G''') → poly3''', e''', g''', d_2, e_2, m''', l''', k''', j''', i''', h'''
  136. Rotate(G_1, (d4 * 60°), F) → F_2
  137. Rotate(H_1, (d4 * 60°), F) → G_2
  138. Rotate(I_1, (d4 * 60°), F) → H_2
  139. Rotate(J_1, (d4 * 60°), F) → I_2
  140. Rotate(K_1, (d4 * 60°), F) → J_2
  141. Rotate(L_1, (d4 * 60°), F) → K_2
  142. Rotate(M_1, (d4 * 60°), F) → L_2
  143. Rotate(N_1, (d4 * 60°), F) → M_2
  144. Rotate(O_1, (d4 * 60°), F) → N_2
  145. Rotate(P_1, (d4 * 60°), F) → O_2
  146. Rotate(Q_1, (d4 * 60°), F) → P_2
  147. Rotate(R_1, (d4 * 60°), F) → Q_2
  148. Rotate(S_1, (d4 * 60°), F) → R_2
  149. Rotate(T_1, (d4 * 60°), F) → S_2
  150. Rotate(U_1, (d4 * 60°), F) → T_2
  151. Rotate(V_1, (d4 * 60°), F) → U_2
  152. Rotate(W_1, (d4 * 60°), F) → V_2
  153. Rotate(Z_1, (d4 * 60°), F) → W_2
  154. Rotate(A_2, (d4 * 60°), F) → Z_2
  155. Rotate(B_2, (d4 * 60°), F) → A_3
  156. Polygon(F_2, G_2, P_2, Q_2, R_2, S_2, T_2, U_2, V_2, W_2, Z_2, A_3, H_2, I_2, J_2, K_2, L_2, M_2, N_2, O_2) → poly1''', f_2, o_2, p_2, q_2, r_2, s_2, t_2, u_2, v_3, w_2, z_2, g_2, a_3, h_2, i_2, j_2, k_2, l_2, m_2, n_2
  157. Rotate(N''', (d4 * 60°), F) → B_3
  158. Rotate(C_2, (d4 * 60°), F) → C_3
  159. Rotate(C''', (d4 * 60°), F) → D_3
  160. Rotate(F''', (d4 * 60°), F) → E_3
  161. Rotate(Z''', (d4 * 60°), F) → F_3
  162. Rotate(W''', (d4 * 60°), F) → G_3
  163. Rotate(V''', (d4 * 60°), F) → H_3
  164. Rotate(U''', (d4 * 60°), F) → I_3
  165. Rotate(T''', (d4 * 60°), F) → J_3
  166. Rotate(S''', (d4 * 60°), F) → K_3
  167. Rotate(R''', (d4 * 60°), F) → L_3
  168. Rotate(Q''', (d4 * 60°), F) → M_3
  169. Rotate(P''', (d4 * 60°), F) → N_3
  170. Rotate(O''', (d4 * 60°), F) → O_3
  171. Polygon(B_3, C_3, L_3, M_3, N_3, O_3, D_3, E_3, F_3, G_3, H_3, I_3, J_3, K_3) → poly2, b_3, k_3, l_3, m_3, n_3, o_3, c_3, d_3, e_3, f_3, g_3, h_3, i_3, j_3
  172. Rotate(E''', (d4 * 60°), F) → P_3
  173. Rotate(D_2, (d4 * 60°), F) → Q_3
  174. Rotate(E_2, (d4 * 60°), F) → R_3
  175. Rotate(M''', (d4 * 60°), F) → S_3
  176. Rotate(L''', (d4 * 60°), F) → T_3
  177. Rotate(K''', (d4 * 60°), F) → U_3
  178. Rotate(J''', (d4 * 60°), F) → V_3
  179. Rotate(I''', (d4 * 60°), F) → W_3
  180. Rotate(H''', (d4 * 60°), F) → Z_3
  181. Rotate(G''', (d4 * 60°), F) → A_4
  182. Polygon(P_3, Q_3, R_3, S_3, T_3, U_3, V_3, W_3, Z_3, A_4) → poly3, p_3, a_4, q_3, r_3, s_3, t_3, u_3, v_4, w_3, z_3
  183. Rotate(F_2, (d5 * 60°), F) → B_4
  184. Rotate(G_2, (d5 * 60°), F) → C_4
  185. Rotate(H_2, (d5 * 60°), F) → D_4
  186. Rotate(I_2, (d5 * 60°), F) → E_4
  187. Rotate(J_2, (d5 * 60°), F) → F_4
  188. Rotate(K_2, (d5 * 60°), F) → G_4
  189. Rotate(L_2, (d5 * 60°), F) → H_4
  190. Rotate(M_2, (d5 * 60°), F) → I_4
  191. Rotate(N_2, (d5 * 60°), F) → J_4
  192. Rotate(O_2, (d5 * 60°), F) → K_4
  193. Rotate(P_2, (d5 * 60°), F) → L_4
  194. Rotate(Q_2, (d5 * 60°), F) → M_4
  195. Rotate(R_2, (d5 * 60°), F) → N_4
  196. Rotate(S_2, (d5 * 60°), F) → O_4
  197. Rotate(T_2, (d5 * 60°), F) → P_4
  198. Rotate(U_2, (d5 * 60°), F) → Q_4
  199. Rotate(V_2, (d5 * 60°), F) → R_4
  200. Rotate(W_2, (d5 * 60°), F) → S_4
  201. Rotate(Z_2, (d5 * 60°), F) → T_4
  202. Rotate(A_3, (d5 * 60°), F) → U_4
  203. Polygon(B_4, C_4, L_4, M_4, N_4, O_4, P_4, Q_4, R_4, S_4, T_4, U_4, D_4, E_4, F_4, G_4, H_4, I_4, J_4, K_4) → poly4, b_4, k_4, l_4, m_4, n_4, o_4, p_4, q_4, r_4, s_4, t_4, c_4, u_4, d_4, e_4, f_4, g_4, h_4, i_4, j_4
  204. Rotate(B_3, (d5 * 60°), F) → V_4
  205. Rotate(C_3, (d5 * 60°), F) → W_4
  206. Rotate(D_3, (d5 * 60°), F) → Z_4
  207. Rotate(E_3, (d5 * 60°), F) → A_5
  208. Rotate(F_3, (d5 * 60°), F) → B_5
  209. Rotate(G_3, (d5 * 60°), F) → C_5
  210. Rotate(H_3, (d5 * 60°), F) → D_5
  211. Rotate(I_3, (d5 * 60°), F) → E_5
  212. Rotate(J_3, (d5 * 60°), F) → F_5
  213. Rotate(K_3, (d5 * 60°), F) → G_5
  214. Rotate(L_3, (d5 * 60°), F) → H_5
  215. Rotate(M_3, (d5 * 60°), F) → I_5
  216. Rotate(N_3, (d5 * 60°), F) → J_5
  217. Rotate(O_3, (d5 * 60°), F) → K_5
  218. Polygon(V_4, W_4, H_5, I_5, J_5, K_5, Z_4, A_5, B_5, C_5, D_5, E_5, F_5, G_5) → poly2'_1, v_5, g_5, h_5, i_5, j_5, k_5, w_4, z_4, a_5, b_5, c_5, d_5, e_5, f_5
  219. Rotate(P_3, (d5 * 60°), F) → L_5
  220. Rotate(Q_3, (d5 * 60°), F) → M_5
  221. Rotate(R_3, (d5 * 60°), F) → N_5
  222. Rotate(S_3, (d5 * 60°), F) → O_5
  223. Rotate(T_3, (d5 * 60°), F) → P_5
  224. Rotate(U_3, (d5 * 60°), F) → Q_5
  225. Rotate(V_3, (d5 * 60°), F) → R_5
  226. Rotate(W_3, (d5 * 60°), F) → S_5
  227. Rotate(Z_3, (d5 * 60°), F) → T_5
  228. Rotate(A_4, (d5 * 60°), F) → U_5
  229. Polygon(L_5, M_5, N_5, O_5, P_5, Q_5, R_5, S_5, T_5, U_5) → poly3'_1, l_5, u_5, m_5, n_5, o_5, p_5, q_5, r_5, s_5, t_5
  230. Rotate(V_4, (d6 * 60°), F) → V_5
  231. Rotate(W_4, (d6 * 60°), F) → W_5
  232. Rotate(Z_4, (d6 * 60°), F) → Z_5
  233. Rotate(A_5, (d6 * 60°), F) → A_6
  234. Rotate(B_5, (d6 * 60°), F) → B_6
  235. Rotate(C_5, (d6 * 60°), F) → C_6
  236. Rotate(D_5, (d6 * 60°), F) → D_6
  237. Rotate(E_5, (d6 * 60°), F) → E_6
  238. Rotate(F_5, (d6 * 60°), F) → F_6
  239. Rotate(G_5, (d6 * 60°), F) → G_6
  240. Rotate(H_5, (d6 * 60°), F) → H_6
  241. Rotate(I_5, (d6 * 60°), F) → I_6
  242. Rotate(J_5, (d6 * 60°), F) → J_6
  243. Rotate(K_5, (d6 * 60°), F) → K_6
  244. Polygon(V_5, W_5, H_6, I_6, J_6, K_6, Z_5, A_6, B_6, C_6, D_6, E_6, F_6, G_6) → poly5, v_6, g_6, h_6, i_6, j_6, k_6, w_5, z_5, a_6, b_6, c_6, d_6, e_6, f_6
  245. Rotate(B_4, (d6 * 60°), F) → L_6
  246. Rotate(C_4, (d6 * 60°), F) → M_6
  247. Rotate(D_4, (d6 * 60°), F) → N_6
  248. Rotate(E_4, (d6 * 60°), F) → O_6
  249. Rotate(F_4, (d6 * 60°), F) → P_6
  250. Rotate(G_4, (d6 * 60°), F) → Q_6
  251. Rotate(H_4, (d6 * 60°), F) → R_6
  252. Rotate(I_4, (d6 * 60°), F) → S_6
  253. Rotate(J_4, (d6 * 60°), F) → T_6
  254. Rotate(K_4, (d6 * 60°), F) → U_6
  255. Rotate(L_4, (d6 * 60°), F) → V_6
  256. Rotate(M_4, (d6 * 60°), F) → W_6
  257. Rotate(N_4, (d6 * 60°), F) → Z_6
  258. Rotate(O_4, (d6 * 60°), F) → A_7
  259. Rotate(P_4, (d6 * 60°), F) → B_7
  260. Rotate(Q_4, (d6 * 60°), F) → C_7
  261. Rotate(R_4, (d6 * 60°), F) → D_7
  262. Rotate(S_4, (d6 * 60°), F) → E_7
  263. Rotate(T_4, (d6 * 60°), F) → F_7
  264. Rotate(U_4, (d6 * 60°), F) → G_7
  265. Polygon(L_6, M_6, V_6, W_6, Z_6, A_7, B_7, C_7, D_7, E_7, F_7, G_7, N_6, O_6, P_6, Q_6, R_6, S_6, T_6, U_6) → poly4', l_6, u_6, v_7, w_6, z_6, a_7, b_7, c_7, d_7, e_7, f_7, m_6, g_7, n_6, o_6, p_6, q_6, r_6, s_6, t_6
  266. Rotate(L_5, (d6 * 60°), F) → H_7
  267. Rotate(M_5, (d6 * 60°), F) → I_7
  268. Rotate(N_5, (d6 * 60°), F) → J_7
  269. Rotate(O_5, (d6 * 60°), F) → K_7
  270. Rotate(P_5, (d6 * 60°), F) → L_7
  271. Rotate(Q_5, (d6 * 60°), F) → M_7
  272. Rotate(R_5, (d6 * 60°), F) → N_7
  273. Rotate(S_5, (d6 * 60°), F) → O_7
  274. Rotate(T_5, (d6 * 60°), F) → P_7
  275. Rotate(U_5, (d6 * 60°), F) → Q_7
  276. Polygon(H_7, I_7, J_7, K_7, L_7, M_7, N_7, O_7, P_7, Q_7) → poly6, h_7, q_7, i_7, j_7, k_7, l_7, m_7, n_7, o_7, p_7
  277. Rotate(N', ((-d7) * 120°), E) → N''_1
  278. Rotate(B_1, ((-d7) * 120°), E) → R_7
  279. Rotate(C', ((-d7) * 120°), E) → C''_1
  280. Rotate(F', ((-d7) * 120°), E) → F''_1
  281. Rotate(Z', ((-d7) * 120°), E) → Z''_1
  282. Rotate(W', ((-d7) * 120°), E) → W''_1
  283. Rotate(V', ((-d7) * 120°), E) → V''_1
  284. Rotate(U', ((-d7) * 120°), E) → U''_1
  285. Rotate(T', ((-d7) * 120°), E) → T''_1
  286. Rotate(S', ((-d7) * 120°), E) → S''_1
  287. Rotate(R', ((-d7) * 120°), E) → R''_1
  288. Rotate(Q', ((-d7) * 120°), E) → Q''_1
  289. Rotate(P', ((-d7) * 120°), E) → P''_1
  290. Rotate(O', ((-d7) * 120°), E) → O''_1
  291. Polygon(N''_1, R_7, R''_1, Q''_1, P''_1, O''_1, C''_1, F''_1, Z''_1, W''_1, V''_1, U''_1, T''_1, S''_1) → poly2''_1, n''_1, s''_1, r''_1, q''_1, p''_1, o''_1, r_7, c''_1, f''_1, z''_1, w''_1, v''_1, u''_1, t''_1
  292. Rotate(E', ((-d7) * 120°), E) → E''_1
  293. Rotate(C_1, ((-d7) * 120°), E) → S_7
  294. Rotate(N'_1, ((-d7) * 120°), E) → T_7
  295. Rotate(M', ((-d7) * 120°), E) → M''_1
  296. Rotate(L', ((-d7) * 120°), E) → L''_1
  297. Rotate(K', ((-d7) * 120°), E) → K''_1
  298. Rotate(J', ((-d7) * 120°), E) → J''_1
  299. Rotate(I', ((-d7) * 120°), E) → I''_1
  300. Rotate(H', ((-d7) * 120°), E) → H''_1
  301. Rotate(G', ((-d7) * 120°), E) → G''_1
  302. Polygon(E''_1, S_7, T_7, M''_1, L''_1, K''_1, J''_1, I''_1, H''_1, G''_1) → poly3''_1, e''_1, g''_1, s_7, t_7, m''_1, l''_1, k''_1, j''_1, i''_1, h''_1
  303. Rotate(F, ((-d7) * 120°), E) → F'_2
  304. Rotate(E, ((-d7) * 120°), E) → E'_2
  305. Rotate(G, ((-d7) * 120°), E) → G'_2
  306. Rotate(H, ((-d7) * 120°), E) → H'_2
  307. Rotate(I, ((-d7) * 120°), E) → I'_2
  308. Rotate(J, ((-d7) * 120°), E) → J'_2
  309. Rotate(K, ((-d7) * 120°), E) → K'_2
  310. Rotate(L, ((-d7) * 120°), E) → L'_2
  311. Rotate(M, ((-d7) * 120°), E) → M'_2
  312. Rotate(N, ((-d7) * 120°), E) → N'_3
  313. Rotate(O, ((-d7) * 120°), E) → O'_2
  314. Rotate(P, ((-d7) * 120°), E) → P'_2
  315. Rotate(Q, ((-d7) * 120°), E) → Q'_2
  316. Rotate(R, ((-d7) * 120°), E) → R'_2
  317. Rotate(S, ((-d7) * 120°), E) → S'_2
  318. Rotate(T, ((-d7) * 120°), E) → T'_2
  319. Rotate(U, ((-d7) * 120°), E) → U'_2
  320. Rotate(V, ((-d7) * 120°), E) → V'_2
  321. Rotate(W, ((-d7) * 120°), E) → W'_2
  322. Rotate(Z, ((-d7) * 120°), E) → Z'_2
  323. Polygon(F'_2, E'_2, O'_2, P'_2, Q'_2, R'_2, S'_2, T'_2, U'_2, V'_2, W'_2, Z'_2, G'_2, H'_2, I'_2, J'_2, K'_2, L'_2, M'_2, N'_3) → poly1'_1, f'_2, n'_3, o'_2, p'_2, q'_2, r'_2, s'_2, t'_2, u'_2, v'_2, w'_2, e'_2, z'_2, g'_2, h'_2, i'_2, j'_2, k'_2, l'_2, m'_2
  324. Rotate(F'_2, ((-d8) * 120°), E) → U_7
  325. Rotate(E'_2, ((-d8) * 120°), E) → V_7
  326. Rotate(G'_2, ((-d8) * 120°), E) → W_7
  327. Rotate(H'_2, ((-d8) * 120°), E) → Z_7
  328. Rotate(I'_2, ((-d8) * 120°), E) → A_8
  329. Rotate(J'_2, ((-d8) * 120°), E) → B_8
  330. Rotate(K'_2, ((-d8) * 120°), E) → C_8
  331. Rotate(L'_2, ((-d8) * 120°), E) → D_8
  332. Rotate(M'_2, ((-d8) * 120°), E) → E_8
  333. Rotate(N'_3, ((-d8) * 120°), E) → F_8
  334. Rotate(O'_2, ((-d8) * 120°), E) → G_8
  335. Rotate(P'_2, ((-d8) * 120°), E) → H_8
  336. Rotate(Q'_2, ((-d8) * 120°), E) → I_8
  337. Rotate(R'_2, ((-d8) * 120°), E) → J_8
  338. Rotate(S'_2, ((-d8) * 120°), E) → K_8
  339. Rotate(T'_2, ((-d8) * 120°), E) → L_8
  340. Rotate(U'_2, ((-d8) * 120°), E) → M_8
  341. Rotate(V'_2, ((-d8) * 120°), E) → N_8
  342. Rotate(W'_2, ((-d8) * 120°), E) → O_8
  343. Rotate(Z'_2, ((-d8) * 120°), E) → P_8
  344. Polygon(U_7, V_7, G_8, H_8, I_8, J_8, K_8, L_8, M_8, N_8, O_8, P_8, W_7, Z_7, A_8, B_8, C_8, D_8, E_8, F_8) → poly7, u_7, f_8, g_8, h_8, i_8, j_8, k_8, l_8, m_8, n_8, o_8, v_8, p_8, w_7, z_7, a_8, b_8, c_8, d_8, e_8
  345. Rotate(N''_1, ((-d8) * 120°), E) → Q_8
  346. Rotate(R_7, ((-d8) * 120°), E) → R_8
  347. Rotate(C''_1, ((-d8) * 120°), E) → S_8
  348. Rotate(F''_1, ((-d8) * 120°), E) → T_8
  349. Rotate(Z''_1, ((-d8) * 120°), E) → U_8
  350. Rotate(W''_1, ((-d8) * 120°), E) → V_8
  351. Rotate(V''_1, ((-d8) * 120°), E) → W_8
  352. Rotate(U''_1, ((-d8) * 120°), E) → Z_8
  353. Rotate(T''_1, ((-d8) * 120°), E) → A_9
  354. Rotate(S''_1, ((-d8) * 120°), E) → B_9
  355. Rotate(R''_1, ((-d8) * 120°), E) → C_9
  356. Rotate(Q''_1, ((-d8) * 120°), E) → D_9
  357. Rotate(P''_1, ((-d8) * 120°), E) → E_9
  358. Rotate(O''_1, ((-d8) * 120°), E) → F_9
  359. Polygon(Q_8, R_8, C_9, D_9, E_9, F_9, S_8, T_8, U_8, V_8, W_8, Z_8, A_9, B_9) → poly8, q_8, b_9, c_9, d_9, e_9, f_9, r_8, s_8, t_8, u_8, v_9, w_8, z_8, a_9
  360. Rotate(E''_1, ((-d8) * 120°), E) → G_9
  361. Rotate(S_7, ((-d8) * 120°), E) → H_9
  362. Rotate(T_7, ((-d8) * 120°), E) → I_9
  363. Rotate(M''_1, ((-d8) * 120°), E) → J_9
  364. Rotate(L''_1, ((-d8) * 120°), E) → K_9
  365. Rotate(K''_1, ((-d8) * 120°), E) → L_9
  366. Rotate(J''_1, ((-d8) * 120°), E) → M_9
  367. Rotate(I''_1, ((-d8) * 120°), E) → N_9
  368. Rotate(H''_1, ((-d8) * 120°), E) → O_9
  369. Rotate(G''_1, ((-d8) * 120°), E) → P_9
  370. Polygon(G_9, H_9, I_9, J_9, K_9, L_9, M_9, N_9, O_9, P_9) → poly9, g_9, p_9, h_9, i_9, j_9, k_9, l_9, m_9, n_9, o_9
  371. Intersect(b'_1, b') → Q_9
  372. Intersect(b, b') → R_9
  373. Intersect(b'_1, b) → S_9
  374. Mirror(R_9, S_9) → T_9
  375. Mirror(S_9, T_9) → U_9
  376. Mirror(Q_9, S_9) → V_9
  377. Vector(V_9, T_9) → d
  378. Translate(S_9, d) → W_9
  379. Mirror(W_9, S_9) → Z_9
  380. Mirror(Z_9, R_9) → A_{10}
  381. Mirror(Z_9, V_9) → B_{10}
  382. Mirror(V_9, B_{10}) → C_{10}
  383. Mirror(V_9, T_9) → D_{10}
  384. Mirror(W_9, D_{10}) → E_{10}
  385. Mirror(U_9, D_{10}) → F_{10}
  386. Mirror(T_9, D_{10}) → G_{10}
  387. Mirror(D_{10}, G_{10}) → H_{10}
  388. Mirror(W_9, F_{10}) → I_{10}
  389. Mirror(H_{10}, I_{10}) → J_{10}
  390. Mirror(I_{10}, J_{10}) → K_{10}
  391. Mirror(J_{10}, K_{10}) → L_{10}
  392. Mirror(G_{10}, F_{10}) → M_{10}
  393. Mirror(F_{10}, M_{10}) → N_{10}
  394. Angle(W_9, Q_9, M_{10}) → α
  395. Angle(T_9, S_9, Q_9) → γ
  396. Vector(W_9, G_{10}) → a_1
  397. Vector(W_9, J_{10}) → u_9
  398. Vector(W_9, N_{10}) → w_9
  399. Vector(W_9, R_9) → z_9
  400. Vector(W_9, V_9) → q_9
  401. Vector(W_9, U_9) → r_9
  402. Midpoint(K_{10}, F_{10}) → O_{10}
  403. Midpoint(F_{10}, E_{10}) → P_{10}
  404. Midpoint(E_{10}, T_9) → Q_{10}
  405. Midpoint(T_9, Z_9) → R_{10}
  406. Midpoint(T_9, F_{10}) → S_{10}
  407. Midpoint(F_{10}, H_{10}) → T_{10}
  408. Midpoint(E_{10}, C_{10}) → U_{10}
  409. Midpoint(C_{10}, T_9) → V_{10}
  410. Min(180, ((a - 9) * 180)) → g5
  411. Rotate(P_3, (-(g5°)), C_3) → B_{11}
  412. Rotate(Q_3, (-(g5°)), C_3) → C_{11}
  413. Rotate(R_3, (-(g5°)), C_3) → D_{11}
  414. Rotate(S_3, (-(g5°)), C_3) → E_{11}
  415. Rotate(T_3, (-(g5°)), C_3) → F_{11}
  416. Rotate(U_3, (-(g5°)), C_3) → G_{11}
  417. Rotate(V_3, (-(g5°)), C_3) → H_{11}
  418. Rotate(W_3, (-(g5°)), C_3) → I_{11}
  419. Rotate(Z_3, (-(g5°)), C_3) → J_{11}
  420. Rotate(A_4, (-(g5°)), C_3) → K_{11}
  421. Polygon(B_{11}, C_{11}, D_{11}, E_{11}, F_{11}, G_{11}, H_{11}, I_{11}, J_{11}, K_{11}) → poly3'_2, b_{11}, k_{11}, c_{11}, d_{11}, e_{11}, f_{11}, g_{11}, h_{11}, i_{11}, j_{11}
  422. Rotate(F_2, (-(g5°)), C_3) → L_{11}
  423. Rotate(G_2, (-(g5°)), C_3) → M_{11}
  424. Rotate(H_2, (-(g5°)), C_3) → N_{11}
  425. Rotate(I_2, (-(g5°)), C_3) → O_{11}
  426. Rotate(J_2, (-(g5°)), C_3) → P_{11}
  427. Rotate(K_2, (-(g5°)), C_3) → Q_{11}
  428. Rotate(L_2, (-(g5°)), C_3) → R_{11}
  429. Rotate(M_2, (-(g5°)), C_3) → S_{11}
  430. Rotate(N_2, (-(g5°)), C_3) → T_{11}
  431. Rotate(O_2, (-(g5°)), C_3) → U_{11}
  432. Rotate(P_2, (-(g5°)), C_3) → V_{11}
  433. Rotate(Q_2, (-(g5°)), C_3) → W_{11}
  434. Rotate(R_2, (-(g5°)), C_3) → Z_{11}
  435. Rotate(S_2, (-(g5°)), C_3) → A_{12}
  436. Rotate(T_2, (-(g5°)), C_3) → B_{12}
  437. Rotate(U_2, (-(g5°)), C_3) → C_{12}
  438. Rotate(V_2, (-(g5°)), C_3) → D_{12}
  439. Rotate(W_2, (-(g5°)), C_3) → E_{12}
  440. Rotate(Z_2, (-(g5°)), C_3) → F_{12}
  441. Rotate(A_3, (-(g5°)), C_3) → G_{12}
  442. Polygon(L_{11}, M_{11}, V_{11}, W_{11}, Z_{11}, A_{12}, B_{12}, C_{12}, D_{12}, E_{12}, F_{12}, G_{12}, N_{11}, O_{11}, P_{11}, Q_{11}, R_{11}, S_{11}, T_{11}, U_{11}) → poly10, l_{11}, u_{11}, v_{11}, w_{11}, z_{11}, a_{12}, b_{12}, c_{12}, d_{12}, e_{12}, f_{12}, m_{11}, g_{12}, n_{11}, o_{11}, p_{11}, q_{11}, r_{11}, s_{11}, t_{11}
  443. Rotate(B_3, g5°, C_3) → H_{12}
  444. Rotate(C_3, g5°, C_3) → I_{12}
  445. Rotate(D_3, g5°, C_3) → J_{12}
  446. Rotate(E_3, g5°, C_3) → K_{12}
  447. Rotate(F_3, g5°, C_3) → L_{12}
  448. Rotate(G_3, g5°, C_3) → M_{12}
  449. Rotate(H_3, g5°, C_3) → N_{12}
  450. Rotate(I_3, g5°, C_3) → O_{12}
  451. Rotate(J_3, g5°, C_3) → P_{12}
  452. Rotate(K_3, g5°, C_3) → Q_{12}
  453. Rotate(L_3, g5°, C_3) → R_{12}
  454. Rotate(M_3, g5°, C_3) → S_{12}
  455. Rotate(N_3, g5°, C_3) → T_{12}
  456. Rotate(O_3, g5°, C_3) → U_{12}
  457. Rotate(E''', (-(g5°)), C_2) → V_{12}
  458. Rotate(D_2, (-(g5°)), C_2) → W_{12}
  459. Rotate(E_2, (-(g5°)), C_2) → Z_{12}
  460. Rotate(M''', (-(g5°)), C_2) → A_{13}
  461. Rotate(L''', (-(g5°)), C_2) → B_{13}
  462. Rotate(K''', (-(g5°)), C_2) → C_{13}
  463. Rotate(J''', (-(g5°)), C_2) → D_{13}
  464. Rotate(I''', (-(g5°)), C_2) → E_{13}
  465. Rotate(H''', (-(g5°)), C_2) → F_{13}
  466. Rotate(G''', (-(g5°)), C_2) → G_{13}
  467. Polygon(V_{12}, W_{12}, Z_{12}, A_{13}, B_{13}, C_{13}, D_{13}, E_{13}, F_{13}, G_{13}) → poly11, v_{12}, g_{13}, w_{12}, z_{12}, a_{13}, b_{13}, c_{13}, d_{13}, e_{13}, f_{13}
  468. Rotate(G_1, (-(g5°)), C_2) → H_{13}
  469. Rotate(H_1, (-(g5°)), C_2) → I_{13}
  470. Rotate(I_1, (-(g5°)), C_2) → J_{13}
  471. Rotate(J_1, (-(g5°)), C_2) → K_{13}
  472. Rotate(K_1, (-(g5°)), C_2) → L_{13}
  473. Rotate(L_1, (-(g5°)), C_2) → M_{13}
  474. Rotate(M_1, (-(g5°)), C_2) → N_{13}
  475. Rotate(N_1, (-(g5°)), C_2) → O_{13}
  476. Rotate(O_1, (-(g5°)), C_2) → P_{13}
  477. Rotate(P_1, (-(g5°)), C_2) → Q_{13}
  478. Rotate(Q_1, (-(g5°)), C_2) → R_{13}
  479. Rotate(R_1, (-(g5°)), C_2) → S_{13}
  480. Rotate(S_1, (-(g5°)), C_2) → T_{13}
  481. Rotate(T_1, (-(g5°)), C_2) → U_{13}
  482. Rotate(U_1, (-(g5°)), C_2) → V_{13}
  483. Rotate(V_1, (-(g5°)), C_2) → W_{13}
  484. Rotate(W_1, (-(g5°)), C_2) → Z_{13}
  485. Rotate(Z_1, (-(g5°)), C_2) → A_{14}
  486. Rotate(A_2, (-(g5°)), C_2) → B_{14}
  487. Rotate(B_2, (-(g5°)), C_2) → C_{14}
  488. Polygon(H_{13}, I_{13}, R_{13}, S_{13}, T_{13}, U_{13}, V_{13}, W_{13}, Z_{13}, A_{14}, B_{14}, C_{14}, J_{13}, K_{13}, L_{13}, M_{13}, N_{13}, O_{13}, P_{13}, Q_{13}) → poly1'''_1, h_{13}, q_{13}, r_{13}, s_{13}, t_{13}, u_{13}, v_{13}, w_{13}, z_{13}, a_{14}, b_{14}, i_{13}, c_{14}, j_{13}, k_{13}, l_{13}, m_{13}, n_{13}, o_{13}, p_{13}
  489. Rotate(N''', (-(g5°)), C_2) → D_{14}
  490. Rotate(C_2, (-(g5°)), C_2) → E_{14}
  491. Rotate(C''', (-(g5°)), C_2) → F_{14}
  492. Rotate(F''', (-(g5°)), C_2) → G_{14}
  493. Rotate(Z''', (-(g5°)), C_2) → H_{14}
  494. Rotate(W''', (-(g5°)), C_2) → I_{14}
  495. Rotate(V''', (-(g5°)), C_2) → J_{14}
  496. Rotate(U''', (-(g5°)), C_2) → K_{14}
  497. Rotate(T''', (-(g5°)), C_2) → L_{14}
  498. Rotate(S''', (-(g5°)), C_2) → M_{14}
  499. Rotate(R''', (-(g5°)), C_2) → N_{14}
  500. Rotate(Q''', (-(g5°)), C_2) → O_{14}
  501. Rotate(P''', (-(g5°)), C_2) → P_{14}
  502. Rotate(O''', (-(g5°)), C_2) → Q_{14}
  503. Polygon(D_{14}, E_{14}, N_{14}, O_{14}, P_{14}, Q_{14}, F_{14}, G_{14}, H_{14}, I_{14}, J_{14}, K_{14}, L_{14}, M_{14}) → poly12, d_{14}, m_{14}, n_{14}, o_{14}, p_{14}, q_{14}, e_{14}, f_{14}, g_{14}, h_{14}, i_{14}, j_{14}, k_{14}, l_{14}
  504. Rotate(E'', (-(g5°)), D_1) → E'''_1
  505. Rotate(E_1, (-(g5°)), D_1) → R_{14}
  506. Rotate(F_1, (-(g5°)), D_1) → S_{14}
  507. Rotate(M'', (-(g5°)), D_1) → M'''_1
  508. Rotate(L'', (-(g5°)), D_1) → L'''_1
  509. Rotate(K'', (-(g5°)), D_1) → K'''_1
  510. Rotate(J'', (-(g5°)), D_1) → J'''_1
  511. Rotate(I'', (-(g5°)), D_1) → I'''_1
  512. Rotate(H'', (-(g5°)), D_1) → H'''_1
  513. Rotate(G'', (-(g5°)), D_1) → G'''_1
  514. Polygon(E'''_1, R_{14}, S_{14}, M'''_1, L'''_1, K'''_1, J'''_1, I'''_1, H'''_1, G'''_1) → poly3'''_1, e'''_1, g'''_1, r_{14}, s_{14}, m'''_1, l'''_1, k'''_1, j'''_1, i'''_1, h'''_1
  515. Rotate(N'', (-(g5°)), D_1) → N'''_1
  516. Rotate(D_1, (-(g5°)), D_1) → T_{14}
  517. Rotate(C'', (-(g5°)), D_1) → C'''_1
  518. Rotate(F'', (-(g5°)), D_1) → F'''_1
  519. Rotate(Z'', (-(g5°)), D_1) → Z'''_1
  520. Rotate(W'', (-(g5°)), D_1) → W'''_1
  521. Rotate(V'', (-(g5°)), D_1) → V'''_1
  522. Rotate(U'', (-(g5°)), D_1) → U'''_1
  523. Rotate(T'', (-(g5°)), D_1) → T'''_1
  524. Rotate(S'', (-(g5°)), D_1) → S'''_1
  525. Rotate(R'', (-(g5°)), D_1) → R'''_1
  526. Rotate(Q'', (-(g5°)), D_1) → Q'''_1
  527. Rotate(P'', (-(g5°)), D_1) → P'''_1
  528. Rotate(O'', (-(g5°)), D_1) → O'''_1
  529. Polygon(N'''_1, T_{14}, R'''_1, Q'''_1, P'''_1, O'''_1, C'''_1, F'''_1, Z'''_1, W'''_1, V'''_1, U'''_1, T'''_1, S'''_1) → poly2'''_1, n'''_1, s'''_1, r'''_1, q'''_1, p'''_1, o'''_1, t_{14}, c'''_1, f'''_1, z'''_1, w'''_1, v'''_1, u'''_1, t'''_1
  530. Rotate(F'_1, (-(g5°)), D_1) → U_{14}
  531. Rotate(E'_1, (-(g5°)), D_1) → V_{14}
  532. Rotate(G'_1, (-(g5°)), D_1) → W_{14}
  533. Rotate(H'_1, (-(g5°)), D_1) → Z_{14}
  534. Rotate(I'_1, (-(g5°)), D_1) → A_{15}
  535. Rotate(J'_1, (-(g5°)), D_1) → B_{15}
  536. Rotate(K'_1, (-(g5°)), D_1) → C_{15}
  537. Rotate(L'_1, (-(g5°)), D_1) → D_{15}
  538. Rotate(M'_1, (-(g5°)), D_1) → E_{15}
  539. Rotate(N'_2, (-(g5°)), D_1) → F_{15}
  540. Rotate(O'_1, (-(g5°)), D_1) → G_{15}
  541. Rotate(P'_1, (-(g5°)), D_1) → H_{15}
  542. Rotate(Q'_1, (-(g5°)), D_1) → I_{15}
  543. Rotate(R'_1, (-(g5°)), D_1) → J_{15}
  544. Rotate(S'_1, (-(g5°)), D_1) → K_{15}
  545. Rotate(T'_1, (-(g5°)), D_1) → L_{15}
  546. Rotate(U'_1, (-(g5°)), D_1) → M_{15}
  547. Rotate(V'_1, (-(g5°)), D_1) → N_{15}
  548. Rotate(W'_1, (-(g5°)), D_1) → O_{15}
  549. Rotate(Z'_1, (-(g5°)), D_1) → P_{15}
  550. Polygon(U_{14}, V_{14}, G_{15}, H_{15}, I_{15}, J_{15}, K_{15}, L_{15}, M_{15}, N_{15}, O_{15}, P_{15}, W_{14}, Z_{14}, A_{15}, B_{15}, C_{15}, D_{15}, E_{15}, F_{15}) → poly1''_1, u_{14}, f_{15}, g_{15}, h_{15}, i_{15}, j_{15}, k_{15}, l_{15}, m_{15}, n_{15}, o_{15}, v_{14}, p_{15}, w_{14}, z_{14}, a_{15}, b_{15}, c_{15}, d_{15}, e_{15}
  551. Rotate(E', (-(g5°)), B_1) → E''_2
  552. Rotate(C_1, (-(g5°)), B_1) → Q_{15}
  553. Rotate(N'_1, (-(g5°)), B_1) → R_{15}
  554. Rotate(M', (-(g5°)), B_1) → M''_2
  555. Rotate(L', (-(g5°)), B_1) → L''_2
  556. Rotate(K', (-(g5°)), B_1) → K''_2
  557. Rotate(J', (-(g5°)), B_1) → J''_2
  558. Rotate(I', (-(g5°)), B_1) → I''_2
  559. Rotate(H', (-(g5°)), B_1) → H''_2
  560. Rotate(G', (-(g5°)), B_1) → G''_2
  561. Polygon(E''_2, Q_{15}, R_{15}, M''_2, L''_2, K''_2, J''_2, I''_2, H''_2, G''_2) → poly3''_2, e''_2, g''_2, q_{15}, r_{15}, m''_2, l''_2, k''_2, j''_2, i''_2, h''_2
  562. Rotate(F, (-(g5°)), B_1) → F'_3
  563. Rotate(E, (-(g5°)), B_1) → E'_3
  564. Rotate(G, (-(g5°)), B_1) → G'_3
  565. Rotate(H, (-(g5°)), B_1) → H'_3
  566. Rotate(I, (-(g5°)), B_1) → I'_3
  567. Rotate(J, (-(g5°)), B_1) → J'_3
  568. Rotate(K, (-(g5°)), B_1) → K'_3
  569. Rotate(L, (-(g5°)), B_1) → L'_3
  570. Rotate(M, (-(g5°)), B_1) → M'_3
  571. Rotate(N, (-(g5°)), B_1) → N'_4
  572. Rotate(O, (-(g5°)), B_1) → O'_3
  573. Rotate(P, (-(g5°)), B_1) → P'_3
  574. Rotate(Q, (-(g5°)), B_1) → Q'_3
  575. Rotate(R, (-(g5°)), B_1) → R'_3
  576. Rotate(S, (-(g5°)), B_1) → S'_3
  577. Rotate(T, (-(g5°)), B_1) → T'_3
  578. Rotate(U, (-(g5°)), B_1) → U'_3
  579. Rotate(V, (-(g5°)), B_1) → V'_3
  580. Rotate(W, (-(g5°)), B_1) → W'_3
  581. Rotate(Z, (-(g5°)), B_1) → Z'_3
  582. Polygon(F'_3, E'_3, O'_3, P'_3, Q'_3, R'_3, S'_3, T'_3, U'_3, V'_3, W'_3, Z'_3, G'_3, H'_3, I'_3, J'_3, K'_3, L'_3, M'_3, N'_4) → poly1'_2, f'_3, n'_4, o'_3, p'_3, q'_3, r'_3, s'_3, t'_3, u'_3, v'_3, w'_3, e'_3, z'_3, g'_3, h'_3, i'_3, j'_3, k'_3, l'_3, m'_3
  583. Rotate(N', (-(g5°)), B_1) → N''_2
  584. Rotate(B_1, (-(g5°)), B_1) → S_{15}
  585. Rotate(C', (-(g5°)), B_1) → C''_2
  586. Rotate(F', (-(g5°)), B_1) → F''_2
  587. Rotate(Z', (-(g5°)), B_1) → Z''_2
  588. Rotate(W', (-(g5°)), B_1) → W''_2
  589. Rotate(V', (-(g5°)), B_1) → V''_2
  590. Rotate(U', (-(g5°)), B_1) → U''_2
  591. Rotate(T', (-(g5°)), B_1) → T''_2
  592. Rotate(S', (-(g5°)), B_1) → S''_2
  593. Rotate(R', (-(g5°)), B_1) → R''_2
  594. Rotate(Q', (-(g5°)), B_1) → Q''_2
  595. Rotate(P', (-(g5°)), B_1) → P''_2
  596. Rotate(O', (-(g5°)), B_1) → O''_2
  597. Polygon(N''_2, S_{15}, R''_2, Q''_2, P''_2, O''_2, C''_2, F''_2, Z''_2, W''_2, V''_2, U''_2, T''_2, S''_2) → poly2''_2, n''_2, s''_2, r''_2, q''_2, p''_2, o''_2, s_{15}, c''_2, f''_2, z''_2, w''_2, v''_2, u''_2, t''_2
  598. Rotate(B_3, (-(g5°)), C_3) → T_{15}
  599. Rotate(C_3, (-(g5°)), C_3) → U_{15}
  600. Rotate(D_3, (-(g5°)), C_3) → V_{15}
  601. Rotate(E_3, (-(g5°)), C_3) → W_{15}
  602. Rotate(F_3, (-(g5°)), C_3) → Z_{15}
  603. Rotate(G_3, (-(g5°)), C_3) → A_{16}
  604. Rotate(H_3, (-(g5°)), C_3) → B_{16}
  605. Rotate(I_3, (-(g5°)), C_3) → C_{16}
  606. Rotate(J_3, (-(g5°)), C_3) → D_{16}
  607. Rotate(K_3, (-(g5°)), C_3) → E_{16}
  608. Rotate(L_3, (-(g5°)), C_3) → F_{16}
  609. Rotate(M_3, (-(g5°)), C_3) → G_{16}
  610. Rotate(N_3, (-(g5°)), C_3) → H_{16}
  611. Rotate(O_3, (-(g5°)), C_3) → I_{16}
  612. Polygon(T_{15}, U_{15}, F_{16}, G_{16}, H_{16}, I_{16}, V_{15}, W_{15}, Z_{15}, A_{16}, B_{16}, C_{16}, D_{16}, E_{16}) → poly2'_2, t_{15}, e_{16}, f_{16}, g_{16}, h_{16}, i_{16}, u_{15}, v_{15}, w_{15}, z_{15}, a_{16}, b_{16}, c_{16}, d_{16}
  613. Rotate(B_4, g5°, W_4) → J_{16}
  614. Rotate(C_4, g5°, W_4) → K_{16}
  615. Rotate(D_4, g5°, W_4) → L_{16}
  616. Rotate(E_4, g5°, W_4) → M_{16}
  617. Rotate(F_4, g5°, W_4) → N_{16}
  618. Rotate(G_4, g5°, W_4) → O_{16}
  619. Rotate(H_4, g5°, W_4) → P_{16}
  620. Rotate(I_4, g5°, W_4) → Q_{16}
  621. Rotate(J_4, g5°, W_4) → R_{16}
  622. Rotate(K_4, g5°, W_4) → S_{16}
  623. Rotate(L_4, g5°, W_4) → T_{16}
  624. Rotate(M_4, g5°, W_4) → U_{16}
  625. Rotate(N_4, g5°, W_4) → V_{16}
  626. Rotate(O_4, g5°, W_4) → W_{16}
  627. Rotate(P_4, g5°, W_4) → Z_{16}
  628. Rotate(Q_4, g5°, W_4) → A_{17}
  629. Rotate(R_4, g5°, W_4) → B_{17}
  630. Rotate(S_4, g5°, W_4) → C_{17}
  631. Rotate(T_4, g5°, W_4) → D_{17}
  632. Rotate(U_4, g5°, W_4) → E_{17}
  633. Rotate(L_5, g5°, W_4) → F_{17}
  634. Rotate(M_5, g5°, W_4) → G_{17}
  635. Rotate(N_5, g5°, W_4) → H_{17}
  636. Rotate(O_5, g5°, W_4) → I_{17}
  637. Rotate(P_5, g5°, W_4) → J_{17}
  638. Rotate(Q_5, g5°, W_4) → K_{17}
  639. Rotate(R_5, g5°, W_4) → L_{17}
  640. Rotate(S_5, g5°, W_4) → M_{17}
  641. Rotate(T_5, g5°, W_4) → N_{17}
  642. Rotate(U_5, g5°, W_4) → O_{17}
  643. Rotate(V_4, g5°, W_4) → P_{17}
  644. Rotate(W_4, g5°, W_4) → Q_{17}
  645. Rotate(Z_4, g5°, W_4) → R_{17}
  646. Rotate(A_5, g5°, W_4) → S_{17}
  647. Rotate(B_5, g5°, W_4) → T_{17}
  648. Rotate(C_5, g5°, W_4) → U_{17}
  649. Rotate(D_5, g5°, W_4) → V_{17}
  650. Rotate(E_5, g5°, W_4) → W_{17}
  651. Rotate(F_5, g5°, W_4) → Z_{17}
  652. Rotate(G_5, g5°, W_4) → A_{18}
  653. Rotate(H_5, g5°, W_4) → B_{18}
  654. Rotate(I_5, g5°, W_4) → C_{18}
  655. Rotate(J_5, g5°, W_4) → D_{18}
  656. Rotate(K_5, g5°, W_4) → E_{18}
  657. Rotate(L_5, (-(g5°)), W_4) → F_{18}
  658. Rotate(M_5, (-(g5°)), W_4) → G_{18}
  659. Rotate(N_5, (-(g5°)), W_4) → H_{18}
  660. Rotate(O_5, (-(g5°)), W_4) → I_{18}
  661. Rotate(P_5, (-(g5°)), W_4) → J_{18}
  662. Rotate(Q_5, (-(g5°)), W_4) → K_{18}
  663. Rotate(R_5, (-(g5°)), W_4) → L_{18}
  664. Rotate(S_5, (-(g5°)), W_4) → M_{18}
  665. Rotate(T_5, (-(g5°)), W_4) → N_{18}
  666. Rotate(U_5, (-(g5°)), W_4) → O_{18}
  667. Polygon(F_{18}, G_{18}, H_{18}, I_{18}, J_{18}, K_{18}, L_{18}, M_{18}, N_{18}, O_{18}) → poly13, f_{18}, o_{18}, g_{18}, h_{18}, i_{18}, j_{18}, k_{18}, l_{18}, m_{18}, n_{18}
  668. Rotate(V_4, (-(g5°)), W_4) → P_{18}
  669. Rotate(W_4, (-(g5°)), W_4) → Q_{18}
  670. Rotate(Z_4, (-(g5°)), W_4) → R_{18}
  671. Rotate(A_5, (-(g5°)), W_4) → S_{18}
  672. Rotate(B_5, (-(g5°)), W_4) → T_{18}
  673. Rotate(C_5, (-(g5°)), W_4) → U_{18}
  674. Rotate(D_5, (-(g5°)), W_4) → V_{18}
  675. Rotate(E_5, (-(g5°)), W_4) → W_{18}
  676. Rotate(F_5, (-(g5°)), W_4) → Z_{18}
  677. Rotate(G_5, (-(g5°)), W_4) → A_{19}
  678. Rotate(H_5, (-(g5°)), W_4) → B_{19}
  679. Rotate(I_5, (-(g5°)), W_4) → C_{19}
  680. Rotate(J_5, (-(g5°)), W_4) → D_{19}
  681. Rotate(K_5, (-(g5°)), W_4) → E_{19}
  682. Polygon(P_{18}, Q_{18}, B_{19}, C_{19}, D_{19}, E_{19}, R_{18}, S_{18}, T_{18}, U_{18}, V_{18}, W_{18}, Z_{18}, A_{19}) → poly14, p_{18}, a_{19}, b_{19}, c_{19}, d_{19}, e_{19}, q_{18}, r_{18}, s_{18}, t_{18}, u_{18}, v_{18}, w_{18}, z_{18}
  683. Rotate(B_4, (-(g5°)), W_4) → F_{19}
  684. Rotate(C_4, (-(g5°)), W_4) → G_{19}
  685. Rotate(D_4, (-(g5°)), W_4) → H_{19}
  686. Rotate(E_4, (-(g5°)), W_4) → I_{19}
  687. Rotate(F_4, (-(g5°)), W_4) → J_{19}
  688. Rotate(G_4, (-(g5°)), W_4) → K_{19}
  689. Rotate(H_4, (-(g5°)), W_4) → L_{19}
  690. Rotate(I_4, (-(g5°)), W_4) → M_{19}
  691. Rotate(J_4, (-(g5°)), W_4) → N_{19}
  692. Rotate(K_4, (-(g5°)), W_4) → O_{19}
  693. Rotate(L_4, (-(g5°)), W_4) → P_{19}
  694. Rotate(M_4, (-(g5°)), W_4) → Q_{19}
  695. Rotate(N_4, (-(g5°)), W_4) → R_{19}
  696. Rotate(O_4, (-(g5°)), W_4) → S_{19}
  697. Rotate(P_4, (-(g5°)), W_4) → T_{19}
  698. Rotate(Q_4, (-(g5°)), W_4) → U_{19}
  699. Rotate(R_4, (-(g5°)), W_4) → V_{19}
  700. Rotate(S_4, (-(g5°)), W_4) → W_{19}
  701. Rotate(T_4, (-(g5°)), W_4) → Z_{19}
  702. Rotate(U_4, (-(g5°)), W_4) → A_{20}
  703. Polygon(F_{19}, G_{19}, P_{19}, Q_{19}, R_{19}, S_{19}, T_{19}, U_{19}, V_{19}, W_{19}, Z_{19}, A_{20}, H_{19}, I_{19}, J_{19}, K_{19}, L_{19}, M_{19}, N_{19}, O_{19}) → poly4'_1, f_{19}, o_{19}, p_{19}, q_{19}, r_{19}, s_{19}, t_{19}, u_{19}, v_{19}, w_{19}, z_{19}, g_{19}, a_{20}, h_{19}, i_{19}, j_{19}, k_{19}, l_{19}, m_{19}, n_{19}
  704. Rotate(L_6, (-(g5°)), W_5) → B_{20}
  705. Rotate(M_6, (-(g5°)), W_5) → C_{20}
  706. Rotate(N_6, (-(g5°)), W_5) → D_{20}
  707. Rotate(O_6, (-(g5°)), W_5) → E_{20}
  708. Rotate(P_6, (-(g5°)), W_5) → F_{20}
  709. Rotate(Q_6, (-(g5°)), W_5) → G_{20}
  710. Rotate(R_6, (-(g5°)), W_5) → H_{20}
  711. Rotate(S_6, (-(g5°)), W_5) → I_{20}
  712. Rotate(T_6, (-(g5°)), W_5) → J_{20}
  713. Rotate(U_6, (-(g5°)), W_5) → K_{20}
  714. Rotate(V_6, (-(g5°)), W_5) → L_{20}
  715. Rotate(W_6, (-(g5°)), W_5) → M_{20}
  716. Rotate(Z_6, (-(g5°)), W_5) → N_{20}
  717. Rotate(A_7, (-(g5°)), W_5) → O_{20}
  718. Rotate(B_7, (-(g5°)), W_5) → P_{20}
  719. Rotate(C_7, (-(g5°)), W_5) → Q_{20}
  720. Rotate(D_7, (-(g5°)), W_5) → R_{20}
  721. Rotate(E_7, (-(g5°)), W_5) → S_{20}
  722. Rotate(F_7, (-(g5°)), W_5) → T_{20}
  723. Rotate(G_7, (-(g5°)), W_5) → U_{20}
  724. Polygon(B_{20}, C_{20}, L_{20}, M_{20}, N_{20}, O_{20}, P_{20}, Q_{20}, R_{20}, S_{20}, T_{20}, U_{20}, D_{20}, E_{20}, F_{20}, G_{20}, H_{20}, I_{20}, J_{20}, K_{20}) → poly4'', b_{20}, k_{20}, l_{20}, m_{20}, n_{20}, o_{20}, p_{20}, q_{20}, r_{20}, s_{20}, t_{20}, c_{20}, u_{20}, d_{20}, e_{20}, f_{20}, g_{20}, h_{20}, i_{20}, j_{20}
  725. Rotate(V_5, (-(g5°)), W_5) → V_{20}
  726. Rotate(W_5, (-(g5°)), W_5) → W_{20}
  727. Rotate(Z_5, (-(g5°)), W_5) → Z_{20}
  728. Rotate(A_6, (-(g5°)), W_5) → A_{21}
  729. Rotate(B_6, (-(g5°)), W_5) → B_{21}
  730. Rotate(C_6, (-(g5°)), W_5) → C_{21}
  731. Rotate(D_6, (-(g5°)), W_5) → D_{21}
  732. Rotate(E_6, (-(g5°)), W_5) → E_{21}
  733. Rotate(F_6, (-(g5°)), W_5) → F_{21}
  734. Rotate(G_6, (-(g5°)), W_5) → G_{21}
  735. Rotate(H_6, (-(g5°)), W_5) → H_{21}
  736. Rotate(I_6, (-(g5°)), W_5) → I_{21}
  737. Rotate(J_6, (-(g5°)), W_5) → J_{21}
  738. Rotate(K_6, (-(g5°)), W_5) → K_{21}
  739. Polygon(V_{20}, W_{20}, H_{21}, I_{21}, J_{21}, K_{21}, Z_{20}, A_{21}, B_{21}, C_{21}, D_{21}, E_{21}, F_{21}, G_{21}) → poly5', v_{20}, g_{21}, h_{21}, i_{21}, j_{21}, k_{21}, w_{20}, z_{20}, a_{21}, b_{21}, c_{21}, d_{21}, e_{21}, f_{21}
  740. Rotate(H_7, (-(g5°)), W_5) → L_{21}
  741. Rotate(I_7, (-(g5°)), W_5) → M_{21}
  742. Rotate(J_7, (-(g5°)), W_5) → N_{21}
  743. Rotate(K_7, (-(g5°)), W_5) → O_{21}
  744. Rotate(L_7, (-(g5°)), W_5) → P_{21}
  745. Rotate(M_7, (-(g5°)), W_5) → Q_{21}
  746. Rotate(N_7, (-(g5°)), W_5) → R_{21}
  747. Rotate(O_7, (-(g5°)), W_5) → S_{21}
  748. Rotate(P_7, (-(g5°)), W_5) → T_{21}
  749. Rotate(Q_7, (-(g5°)), W_5) → U_{21}
  750. Polygon(L_{21}, M_{21}, N_{21}, O_{21}, P_{21}, Q_{21}, R_{21}, S_{21}, T_{21}, U_{21}) → poly6', l_{21}, u_{21}, m_{21}, n_{21}, o_{21}, p_{21}, q_{21}, r_{21}, s_{21}, t_{21}
  751. Midpoint(W_9, S_9) → V_{21}
  752. Midpoint(W_9, M_{10}) → W_{21}
  753. Midpoint(M_{10}, N_{10}) → Z_{21}
  754. Midpoint(N_{10}, A_{10}) → A_{22}
  755. Midpoint(R_9, A_{10}) → C_{22}
  756. Midpoint(N_{10}, L_{10}) → D_{22}

AI Drawing Prompt Reference

Draw a plane figure with a central rotation reference point. Start by defining an initial line determined by two points, then rotate that line around the chosen center by a fixed angle to obtain a second corresponding line. Use the intersection of the rotated line with its companion (from further rotation) as the main construction core. With this core and the rotated endpoint positions, connect points to form a first polygonal outline. Next, generate additional symmetric vertex sets by repeatedly rotating those same reference vertices around the same center by set angles, and connect the resulting points to build a second polygon with many vertices. Finally, perform another round of fixed-angle rotations around a second reference point to create further corresponding point sets, then connect them in order to form a third polygon, producing an Escher-like pattern with multi-rotation symmetry.
The prompt above was compiled from the original drawing commands and is for reference only.