平面图案群

平面图案群
几何画板及绘图内容加载中,请稍等……
2015-06-27 11:08
所属专题 Transformations
这个范例展示了17种不同的平面图案群,这些图案在两个方向上重复。它涉及平面图形和几何变换的概念。通过使用GeoGebra命令如Line, Vector, Point等,可以构造这些图案。适合中学数学教学和学习。

GeoGebra 命令及参数

  1. Line(A, C) → e
  2. Vector(A, C) → v
  3. Point(OrthogonalLine[A, v]) → G
  4. PointIn(Polygon[A, G, I_{23}, C]) → H
  5. Mirror(H + v, Line[Midpoint[A, G], v]) → K_5
  6. Translate(Polygon[Mirror[A, Line[Midpoint[A, G], v]], Mirror[H, Line[Midpoint[A, G], v]], Mirror[G, Line[Midpoint[A, G], v]], Mirror[I_{23}, Line[Midpoint[A, G], v]], Mirror[K_5, Line[Midpoint[A, G], v]], Mirror[C, Line[Midpoint[A, G], v]]], v) → poly50
  7. Vector(A, G) → h
  8. PointIn(Polygon[Translate[A, h], Translate[C, h], Translate[H, h]]) → I
  9. Vector(A, B) → u
  10. PointIn(Polygon[B, D_2, D_2 + u, B + u]) → D
  11. PointIn(Polygon[C, D_2, D_2 + v, C + v]) → E
  12. PointIn(Polygon[A, C, L_3, V_1]) → M
  13. Polygon(A, M, V_1) → poly13, v_5, a_8, m_5
  14. Point(Ray[Midpoint[A, C], Midpoint[A, C] + OrthogonalVector[v]]) → J
  15. PointIn(Polygon[A, J, C]) → K
  16. Rotate(K, 180*°, Midpoint[A, C]) → W_1
  17. OrthogonalLine(B, e) → g
  18. Intersect(g, e) → G_2
  19. Vector(G_2, B) → w
  20. Mirror(B, e) → B'_1
  21. Mirror(C, e) → C'_1
  22. Mirror(A, e) → A'_1
  23. Polygon(A, D - u, C, E, D_2, D, B, E - v) → poly1, a, b, c, d, q_{22}, r_{22}, s_{22}, t_{22}
  24. Mirror(D_2, e) → D'_1
  25. Midpoint(C, D_2) → E_2
  26. PointIn(poly1) → F
  27. Rotate(F, 180*°, E_2) → F'
  28. Polygon(A, D - u, C, F, F', D_2, D, B) → poly2, f, a_1, b_1, c_1, d_1, d_{23}, g_{23}, r_{23}
  29. Rotate(A, 180*°, E_2) → A'
  30. Rotate(C, 180*°, E_2) → C'
  31. Rotate(F, 180*°, E_2) → F'_1
  32. Rotate(F', 180*°, E_2) → F''
  33. Rotate(D_2, 180*°, E_2) → D'
  34. Rotate(B, 180*°, E_2) → B'
  35. Rotate(poly2, 180*°, E_2) → poly2'
  36. Sequence(Sequence[Translate[{poly2, poly2'}, Vector[(i * u) + ((2 * j) * v)]], i, (-n), n], j, (-n), n) → list2
  37. Polygon(A, H, G, I, I_{23}, K_5, C, I - h) → poly3, i, j, k, h_1, a_2, c_2, k_{12}, k_{23}
  38. Translate(Mirror[poly3, Line[Midpoint[A, G], v]], v) → poly4
  39. Sequence(Sequence[Translate[{poly3, poly4}, Vector[(i * h) + ((2 * j) * v)]], i, (-n), n], j, (-n), n) → list4
  40. Mirror(A, e) → A'_2
  41. Mirror(H, e) → J'
  42. Mirror(G, e) → H'
  43. Mirror(I_{23}, e) → I'
  44. Mirror(K_5, e) → K'
  45. Mirror(C, e) → C'_2
  46. Mirror(poly50, e) → poly4'
  47. Polygon(Mirror[A, e], Mirror[H, e], Mirror[G, e], Mirror[I_{23}, e], Mirror[K_5, e], Mirror[C, e]) → poly3', l_{23}, n_{23}, p_{23}, q_{23}, s_{23}, t_{23}
  48. Polygon(A, G, H, C) → poly5, t, e_1, f_1, g_1
  49. Polygon(G, I_{23}, C, H) → poly6, i_1, j_1, k_1, m_1
  50. OrthogonalLine(C, e) → l
  51. Mirror(A, l) → A'_3
  52. Mirror(H, l) → J'_1
  53. Mirror(C, l) → C'_3
  54. Mirror(A, l) → A'_4
  55. Mirror(G, l) → H'_1
  56. Mirror(I_{23}, l) → I'_1
  57. Mirror(C, l) → C'_4
  58. Mirror(H, l) → J'_2
  59. Mirror(A'_4, e) → L_5
  60. Mirror(H'_1, e) → M_7
  61. Mirror(I'_1, e) → N_{16}
  62. Mirror(C'_4, e) → O_{22}
  63. Mirror(J'_2, e) → P_{22}
  64. Mirror(A'_3, e) → Q_{22}
  65. Mirror(J'_1, e) → R_{22}
  66. Mirror(C'_3, e) → S_{22}
  67. Mirror(L_5, l) → L'
  68. Mirror(M_7, l) → M'
  69. Mirror(N_{16}, l) → N'
  70. Mirror(O_{22}, l) → O'
  71. Mirror(P_{22}, l) → P'
  72. Mirror(Q_{22}, l) → Q'
  73. Mirror(R_{22}, l) → R'
  74. Mirror(S_{22}, l) → S'
  75. Mirror(G, l) → H'_2
  76. Mirror(I_{23}, l) → I'_2
  77. Mirror(C, l) → C'_5
  78. Mirror(H, l) → J'_3
  79. Polygon(H'_2, I'_2, C'_5, J'_3) → poly6', h'_2, i'_2, c'_5, j'_3
  80. Mirror(A, l) → A'_5
  81. Mirror(G, l) → H'_3
  82. Mirror(H, l) → J'_4
  83. Mirror(C, l) → C'_6
  84. Polygon(A'_5, H'_3, J'_4, C'_6) → poly5', a'_5, h'_3, j'_4, c'_6
  85. Mirror(H'_2, e) → T_{22}
  86. Mirror(I'_2, e) → U
  87. Mirror(C'_5, e) → V_{22}
  88. Mirror(J'_3, e) → Z_{22}
  89. Polygon(T_{22}, U, V_{22}, Z_{22}) → poly6'', t_1, u_1, v_1, z_1
  90. Mirror(A'_5, e) → A_1
  91. Mirror(H'_3, e) → B_1
  92. Mirror(J'_4, e) → C_1
  93. Mirror(C'_6, e) → D_1
  94. Polygon(A_1, B_1, C_1, D_1) → poly5'', a_3, b_2, c_3, d_2
  95. Mirror(A_1, l) → E_1
  96. Mirror(B_1, l) → F_1
  97. Mirror(C_1, l) → G_1
  98. Mirror(D_1, l) → H_1
  99. Polygon(E_1, F_1, G_1, H_1) → poly5''', e_2, f_2, g_2, h_2
  100. Mirror(T_{22}, l) → T'
  101. Mirror(U, l) → U'
  102. Mirror(V_{22}, l) → V'
  103. Mirror(Z_{22}, l) → Z'
  104. Polygon(T', U', V', Z') → poly6''', t', u', v', z'
  105. Sequence(Sequence[Translate[{poly5, poly5', poly5'', poly5''', poly6, poly6', poly6'', poly6'''}, Vector[((i * 2) * h) + ((2 * j) * v)]], i, (-n), n], j, (-n), n) → list6
  106. Rotate(F, 180*°, E_2) → F'_2
  107. Polygon(A, B, D_2, F'_2, F, C) → poly7, m, p, q, r, s, l_1
  108. Rotate(A, 180*°, E_2) → A'_6
  109. Rotate(B, 180*°, E_2) → B'_2
  110. Rotate(D_2, 180*°, E_2) → D'_2
  111. Rotate(F'_2, 180*°, E_2) → I_1
  112. Rotate(F, 180*°, E_2) → F'_3
  113. Rotate(C, 180*°, E_2) → C'_7
  114. Polygon(A'_6, B'_2, D'_2, I_1, F'_3, C'_7) → poly7', a'_6, b'_2, d'_2, i_2, f'_3, c'_7
  115. Mirror(A'_6, e) → J_1
  116. Mirror(B'_2, e) → K_1
  117. Mirror(D'_2, e) → L_1
  118. Mirror(I_1, e) → M_1
  119. Mirror(F'_3, e) → N_1
  120. Mirror(C'_7, e) → O_1
  121. Polygon(J_1, K_1, L_1, M_1, N_1, O_1) → poly7'', j_2, k_2, l_2, m_2, n_1, o_1
  122. Rotate(J_1, 180*°, Mirror[E_2, e]) → P_1
  123. Rotate(K_1, 180*°, Mirror[E_2, e]) → Q_1
  124. Rotate(L_1, 180*°, Mirror[E_2, e]) → R_1
  125. Rotate(M_1, 180*°, Mirror[E_2, e]) → S_1
  126. Rotate(N_1, 180*°, Mirror[E_2, e]) → T_1
  127. Rotate(O_1, 180*°, Mirror[E_2, e]) → U_1
  128. Polygon(P_1, Q_1, R_1, S_1, T_1, U_1) → poly7''', p_1, q_1, r_1, s_1, t_2, u_2
  129. Polygon(A, J, C, W_1, K) → poly8, n_2, p_2, q_2, r_2, s_2
  130. Sequence(Sequence[Translate[{poly7, poly7', poly7'', poly7'''}, Vector[(i * Vector[Mirror[B, e], B]) + ((2 * j) * v)]], i, (-n), n], j, (-n), n) → list7
  131. Rotate(A, 180*°, Midpoint[A, C]) → A'_7
  132. Rotate(J, 180*°, Midpoint[A, C]) → A_2
  133. Rotate(C, 180*°, Midpoint[A, C]) → C'_8
  134. Rotate(W_1, 180*°, Midpoint[A, C]) → B_2
  135. Rotate(K, 180*°, Midpoint[A, C]) → C_2
  136. Polygon(A'_7, A_2, C'_8, B_2, C_2) → poly8', a'_7, a_4, c'_8, b_3, c_4
  137. Translate(Polygon[Mirror[A, OrthogonalLine[Midpoint[J, Midpoint[A, C]], g]], Mirror[J, OrthogonalLine[Midpoint[J, Midpoint[A, C]], g]], Mirror[C, OrthogonalLine[Midpoint[J, Midpoint[A, C]], g]], Mirror[W_1, OrthogonalLine[Midpoint[J, Midpoint[A, C]], g]], Mirror[K, OrthogonalLine[Midpoint[J, Midpoint[A, C]], g]]], Vector[(0.5 * v)]) → poly10
  138. Rotate(poly10, 180*°, Translate[Mirror[Midpoint[A, C], OrthogonalLine[Midpoint[J, Midpoint[A, C]], g]], Vector[(0.5 * v)]]) → poly10'
  139. Sequence(Sequence[Translate[{poly8, poly8', poly10, poly10'}, Vector[((i * 2) * Vector[Midpoint[A, C], J]) + (j * v)]], i, (-n), n], j, (-n), n) → list8
  140. Midpoint(G, C) → J_4
  141. PointIn(Polygon[A, G, C]) → L
  142. Rotate(L, 180*°, J_4) → Z_1
  143. Polygon(A, C, L, Z_1, G) → poly9, a_5, c_5, v_2, z_2, e_3
  144. Rotate(A, 180*°, J_4) → A'_8
  145. Rotate(C, 180*°, J_4) → C'_9
  146. Rotate(L, 180*°, J_4) → F_2
  147. Rotate(Z_1, 180*°, J_4) → H_2
  148. Rotate(G, 180*°, J_4) → E'
  149. Polygon(A'_8, C'_9, F_2, H_2, E') → poly9', a'_8, c'_9, f_3, h_3, e'
  150. Mirror(A'_8, e) → I_2
  151. Mirror(C'_9, e) → J_2
  152. Mirror(F_2, e) → K_2
  153. Mirror(H_2, e) → L_2
  154. Mirror(E', e) → E''
  155. Polygon(I_2, J_2, K_2, L_2, E'') → poly9'', i_3, j_3, k_3, l_3, e''
  156. Mirror(A'_8, l) → M_2
  157. Mirror(C'_9, l) → N_2
  158. Mirror(F_2, l) → O_2
  159. Mirror(H_2, l) → P_2
  160. Mirror(E', l) → E''_1
  161. Polygon(M_2, N_2, O_2, P_2, E''_1) → poly9''_1, m_3, n_3, o_2, p_3, e''_1
  162. Mirror(I_2, l) → Q_2
  163. Mirror(J_2, l) → R_2
  164. Mirror(K_2, l) → S_2
  165. Mirror(L_2, l) → T_2
  166. Mirror(E'', l) → E'''
  167. Polygon(Q_2, R_2, S_2, T_2, E''') → poly9''', q_3, r_3, s_3, t_3, e'''
  168. Rotate(M_2, 180*°, Mirror[J_4, l]) → U_2
  169. Rotate(N_2, 180*°, Mirror[J_4, l]) → V_2
  170. Rotate(O_2, 180*°, Mirror[J_4, l]) → W_2
  171. Rotate(P_2, 180*°, Mirror[J_4, l]) → Z_2
  172. Rotate(E''_1, 180*°, Mirror[J_4, l]) → A_3
  173. Polygon(U_2, V_2, W_2, Z_2, A_3) → poly11, u_3, v_3, w_2, z_3, a_6
  174. Mirror(U_2, e) → B_3
  175. Mirror(V_2, e) → C_3
  176. Mirror(W_2, e) → D_3
  177. Mirror(Z_2, e) → E_3
  178. Mirror(A_3, e) → F_3
  179. Polygon(B_3, C_3, D_3, E_3, F_3) → poly11', b_4, c_6, d_3, e_4, f_4
  180. Mirror(B_3, l) → G_3
  181. Mirror(C_3, l) → H_3
  182. Mirror(D_3, l) → I_3
  183. Mirror(E_3, l) → J_3
  184. Mirror(F_3, l) → K_3
  185. Polygon(G_3, H_3, I_3, J_3, K_3) → poly11'', g_3, h_4, i_4, j_4, k_4
  186. Sequence(Sequence[Translate[{poly9, poly9', poly9'', poly9''_1, poly9''', poly11, poly11', poly11''}, Vector[((i * 2) * h) + ((2 * j) * v)]], i, (-n), n], j, (-n), n) → list9
  187. Rotate(M, 90*°, L_3) → N_3
  188. PointIn(poly13) → N
  189. Rotate(N, -90*°, A) → P_3
  190. Polygon(A, P_3, C, N_3, L_3, M, V_1, N) → poly12, a_7, p_4, c_7, n_4, l_4, m_4, v_4, o_3
  191. Rotate(A, 90*°, L_3) → A'_9
  192. Rotate(P_3, 90*°, L_3) → Q_3
  193. Rotate(C, 90*°, L_3) → C'_{10}
  194. Rotate(N_3, 90*°, L_3) → R_3
  195. Rotate(L_3, 90*°, L_3) → S_3
  196. Rotate(M, 90*°, L_3) → T_3
  197. Rotate(V_1, 90*°, L_3) → U_3
  198. Rotate(N, 90*°, L_3) → V_3
  199. Polygon(A'_9, Q_3, C'_{10}, R_3, S_3, T_3, U_3, V_3) → poly12', a'_9, q_4, c'_{10}, r_4, s_4, t_4, u_4, v_6
  200. Rotate(A'_9, 90*°, L_3) → W_3
  201. Rotate(Q_3, 90*°, L_3) → Z_3
  202. Rotate(C'_{10}, 90*°, L_3) → A_4
  203. Rotate(R_3, 90*°, L_3) → B_4
  204. Rotate(S_3, 90*°, L_3) → C_4
  205. Rotate(T_3, 90*°, L_3) → D_4
  206. Rotate(U_3, 90*°, L_3) → E_4
  207. Rotate(V_3, 90*°, L_3) → F_4
  208. Polygon(W_3, Z_3, A_4, B_4, C_4, D_4, E_4, F_4) → poly12'', w_3, z_4, a_9, b_5, c_8, d_4, e_5, f_5
  209. Rotate(W_3, 90*°, L_3) → G_4
  210. Rotate(Z_3, 90*°, L_3) → H_4
  211. Rotate(A_4, 90*°, L_3) → I_4
  212. Rotate(B_4, 90*°, L_3) → K_4
  213. Rotate(C_4, 90*°, L_3) → L_4
  214. Rotate(D_4, 90*°, L_3) → M_4
  215. Rotate(E_4, 90*°, L_3) → N_4
  216. Rotate(F_4, 90*°, L_3) → O_4
  217. Polygon(G_4, H_4, I_4, K_4, L_4, M_4, N_4, O_4) → poly12''', g_4, h_5, i_5, k_5, l_5, m_6, n_5, o_4
  218. Sequence(Sequence[Translate[{poly12, poly12', poly12'', poly12'''}, Vector[((i * 2) * OrthogonalVector[Segment[A, C]]) + ((2 * j) * v)]], i, (-n), n], j, (-n), n) → list10
  219. PointIn(Polygon[A, C, V_1]) → P
  220. Polygon(V_1, A, P, C) → poly14, v_7, a_{10}, m_7, c_9
  221. Polygon(A, C, P) → poly15, m_8, a_{11}, c_{10}
  222. OrthogonalVector(Segment[A, C]) → w_1
  223. Line(A, w_1) → d_5
  224. Mirror(V_1, d_5) → O_3
  225. Mirror(A, d_5) → A'_{10}
  226. Mirror(P, d_5) → P_4
  227. Mirror(C, d_5) → C'_{11}
  228. Polygon(O_3, A'_{10}, P_4, C'_{11}) → poly14', o_5, a'_{10}, p_5, c'_{11}
  229. Mirror(A, d_5) → A'_{11}
  230. Mirror(C, d_5) → C'_{12}
  231. Mirror(P, d_5) → Q_4
  232. Polygon(A'_{11}, C'_{12}, Q_4) → poly15', q_5, a'_{11}, c'_{12}
  233. Rotate(O_3, -90*°, V_1) → R_4
  234. Rotate(A'_{10}, -90*°, V_1) → S_4
  235. Rotate(P_4, -90*°, V_1) → T_4
  236. Rotate(C'_{11}, -90*°, V_1) → U_4
  237. Polygon(R_4, S_4, T_4, U_4) → poly14'', r_5, s_5, t_5, u_5
  238. Rotate(A'_{11}, -90*°, V_1) → V_4
  239. Rotate(C'_{12}, -90*°, V_1) → W_4
  240. Rotate(Q_4, -90*°, V_1) → Z_4
  241. Polygon(V_4, W_4, Z_4) → poly15'', z_5, v_8, w_4
  242. Rotate(R_4, -90*°, V_1) → A_5
  243. Rotate(S_4, -90*°, V_1) → B_5
  244. Rotate(T_4, -90*°, V_1) → C_5
  245. Rotate(U_4, -90*°, V_1) → D_5
  246. Polygon(A_5, B_5, C_5, D_5) → poly14''', a_{12}, b_6, c_{11}, d_6
  247. Rotate(V_4, -90*°, V_1) → E_5
  248. Rotate(W_4, -90*°, V_1) → F_5
  249. Rotate(Z_4, -90*°, V_1) → G_5
  250. Polygon(E_5, F_5, G_5) → poly15''', g_5, e_6, f_6
  251. Mirror(A_5, d_5) → H_5
  252. Mirror(B_5, d_5) → I_5
  253. Mirror(C_5, d_5) → J_5
  254. Mirror(D_5, d_5) → M_5
  255. Polygon(H_5, I_5, J_5, M_5) → poly16, h_6, i_6, j_5, m_9
  256. Mirror(E_5, d_5) → N_5
  257. Mirror(F_5, d_5) → O_5
  258. Mirror(G_5, d_5) → P_5
  259. Polygon(N_5, O_5, P_5) → poly17, p_6, n_6, o_6
  260. Rotate(H_5, -90*°, V_1) → Q_5
  261. Rotate(I_5, -90*°, V_1) → R_5
  262. Rotate(J_5, -90*°, V_1) → S_5
  263. Rotate(M_5, -90*°, V_1) → T_5
  264. Polygon(Q_5, R_5, S_5, T_5) → poly16', q_6, r_6, s_6, t_6
  265. Rotate(N_5, -90*°, V_1) → U_5
  266. Rotate(O_5, -90*°, V_1) → V_5
  267. Rotate(P_5, -90*°, V_1) → W_5
  268. Polygon(U_5, V_5, W_5) → poly17', w_5, u_6, v_9
  269. Rotate(A_5, -90*°, V_1) → Z_5
  270. Rotate(B_5, -90*°, V_1) → A_6
  271. Rotate(C_5, -90*°, V_1) → B_6
  272. Rotate(D_5, -90*°, V_1) → C_6
  273. Polygon(Z_5, A_6, B_6, C_6) → poly18, z_6, a_{13}, b_7, c_{12}
  274. Rotate(E_5, -90*°, V_1) → D_6
  275. Rotate(F_5, -90*°, V_1) → E_6
  276. Rotate(G_5, -90*°, V_1) → F_6
  277. Polygon(D_6, E_6, F_6) → poly19, f_7, d_7, e_7
  278. Rotate(H_5, 90*°, V_1) → G_6
  279. Rotate(I_5, 90*°, V_1) → H_6
  280. Rotate(J_5, 90*°, V_1) → I_6
  281. Rotate(M_5, 90*°, V_1) → J_6
  282. Polygon(G_6, H_6, I_6, J_6) → poly16'_1, g_6, h_7, i_7, j_6
  283. Rotate(N_5, 90*°, V_1) → K_6
  284. Rotate(O_5, 90*°, V_1) → L_6
  285. Rotate(P_5, 90*°, V_1) → M_6
  286. Polygon(K_6, L_6, M_6) → poly17'_1, m_{10}, k_6, l_6
  287. Sequence(Sequence[Translate[{poly14, poly14', poly14'', poly14''', poly15, poly15', poly15'', poly15''', poly17'_1, poly17, poly17', poly19, poly16'_1, poly16, poly16', poly18}, Vector[((i * 2) * w_1) + ((2 * j) * v)]], i, (-n), n], j, (-n), n) → list11
  288. Polygon(A, C, N_3, L_3, M, V_1) → poly20, a_{14}, c_{13}, n_7, l_7, k_7, v_{10}
  289. Rotate(A, 90*°, L_3) → A'_{12}
  290. Rotate(C, 90*°, L_3) → C'_{13}
  291. Rotate(N_3, 90*°, L_3) → M_3
  292. Rotate(L_3, 90*°, L_3) → N_6
  293. Rotate(M, 90*°, L_3) → K'_1
  294. Rotate(V_1, 90*°, L_3) → O_6
  295. Polygon(A'_{12}, C'_{13}, M_3, N_6, K'_1, O_6) → poly20', a'_{12}, c'_{13}, m_{11}, n_8, k'_1, o_7
  296. Rotate(A'_{12}, 90*°, L_3) → P_6
  297. Rotate(C'_{13}, 90*°, L_3) → Q_6
  298. Rotate(M_3, 90*°, L_3) → R_6
  299. Rotate(N_6, 90*°, L_3) → S_6
  300. Rotate(K'_1, 90*°, L_3) → T_6
  301. Rotate(O_6, 90*°, L_3) → U_6
  302. Polygon(P_6, Q_6, R_6, S_6, T_6, U_6) → poly20'', p_7, q_7, r_7, s_7, t_7, u_7
  303. Rotate(P_6, 90*°, L_3) → V_6
  304. Rotate(Q_6, 90*°, L_3) → W_6
  305. Rotate(R_6, 90*°, L_3) → Z_6
  306. Rotate(S_6, 90*°, L_3) → A_7
  307. Rotate(T_6, 90*°, L_3) → B_7
  308. Rotate(U_6, 90*°, L_3) → C_7
  309. Polygon(V_6, W_6, Z_6, A_7, B_7, C_7) → poly20''', v_{11}, w_6, z_7, a_{15}, b_8, c_{14}
  310. Line(A, V_1) → g_7
  311. Mirror(V_6, g_7) → D_7
  312. Mirror(W_6, g_7) → E_7
  313. Mirror(Z_6, g_7) → F_7
  314. Mirror(A_7, g_7) → G_7
  315. Mirror(B_7, g_7) → H_7
  316. Mirror(C_7, g_7) → I_7
  317. Polygon(D_7, E_7, F_7, G_7, H_7, I_7) → poly21, d_8, e_8, f_8, g_8, h_8, i_8
  318. Mirror(P_6, g_7) → J_7
  319. Mirror(Q_6, g_7) → K_7
  320. Mirror(R_6, g_7) → L_7
  321. Mirror(S_6, g_7) → N_7
  322. Mirror(T_6, g_7) → O_7
  323. Mirror(U_6, g_7) → P_7
  324. Polygon(J_7, K_7, L_7, N_7, O_7, P_7) → poly20'''_1, j_7, k_8, l_8, n_9, o_8, p_8
  325. Mirror(A'_{12}, e) → Q_7
  326. Mirror(C'_{13}, e) → R_7
  327. Mirror(M_3, e) → S_7
  328. Mirror(N_6, e) → T_7
  329. Mirror(K'_1, e) → U_7
  330. Mirror(O_6, e) → V_7
  331. Polygon(Q_7, R_7, S_7, T_7, U_7, V_7) → poly20''_1, q_8, r_8, s_8, t_8, u_8, v_{12}
  332. Mirror(Q_7, g_7) → W_7
  333. Mirror(R_7, g_7) → Z_7
  334. Mirror(S_7, g_7) → A_8
  335. Mirror(T_7, g_7) → B_8
  336. Mirror(U_7, g_7) → C_8
  337. Mirror(V_7, g_7) → D_8
  338. Polygon(W_7, Z_7, A_8, B_8, C_8, D_8) → poly22, w_7, z_8, a_{16}, b_9, c_{15}, d_9
  339. Mirror(W_7, e) → E_8
  340. Mirror(Z_7, e) → F_8
  341. Mirror(A_8, e) → G_8
  342. Mirror(B_8, e) → H_8
  343. Mirror(C_8, e) → I_8
  344. Mirror(D_8, e) → J_8
  345. Polygon(E_8, F_8, G_8, H_8, I_8, J_8) → poly22', e_9, f_9, g_9, h_9, i_9, j_8
  346. Mirror(P_6, e) → K_8
  347. Mirror(Q_6, e) → L_8
  348. Mirror(R_6, e) → M_8
  349. Mirror(S_6, e) → N_8
  350. Mirror(T_6, e) → O_8
  351. Mirror(U_6, e) → P_8
  352. Polygon(K_8, L_8, M_8, N_8, O_8, P_8) → poly20'''_2, k_9, l_9, m_{12}, n_{10}, o_9, p_9
  353. Mirror(K_8, g_7) → Q_8
  354. Mirror(L_8, g_7) → R_8
  355. Mirror(M_8, g_7) → S_8
  356. Mirror(N_8, g_7) → T_8
  357. Mirror(O_8, g_7) → U_8
  358. Mirror(P_8, g_7) → V_8
  359. Polygon(Q_8, R_8, S_8, T_8, U_8, V_8) → poly23, q_9, r_9, s_9, t_9, u_9, v_{13}
  360. Mirror(A, g_7) → A'_{13}
  361. Mirror(C, g_7) → C'_{14}
  362. Mirror(N_3, g_7) → W_8
  363. Mirror(L_3, g_7) → Z_8
  364. Mirror(M, g_7) → K'_2
  365. Mirror(V_1, g_7) → A_9
  366. Polygon(A'_{13}, C'_{14}, W_8, Z_8, K'_2, A_9) → poly20'_1, a'_{13}, c'_{14}, w_8, z_9, k'_2, a_{17}
  367. Mirror(A'_{13}, e) → B_9
  368. Mirror(C'_{14}, e) → C_9
  369. Mirror(W_8, e) → D_9
  370. Mirror(Z_8, e) → E_9
  371. Mirror(K'_2, e) → F_9
  372. Mirror(A_9, e) → G_9
  373. Polygon(B_9, C_9, D_9, E_9, F_9, G_9) → poly24, b_{10}, c_{16}, d_{10}, e_{10}, f_{10}, g_{10}
  374. Mirror(B_9, g_7) → H_9
  375. Mirror(C_9, g_7) → I_9
  376. Mirror(D_9, g_7) → J_9
  377. Mirror(E_9, g_7) → K_9
  378. Mirror(F_9, g_7) → L_9
  379. Mirror(G_9, g_7) → M_9
  380. Polygon(H_9, I_9, J_9, K_9, L_9, M_9) → poly24', h_{10}, i_{10}, j_9, k_{10}, l_{10}, m_{13}
  381. Mirror(D_7, e) → N_9
  382. Mirror(E_7, e) → O_9
  383. Mirror(F_7, e) → P_9
  384. Mirror(G_7, e) → Q_9
  385. Mirror(H_7, e) → R_9
  386. Mirror(I_7, e) → S_9
  387. Polygon(N_9, O_9, P_9, Q_9, R_9, S_9) → poly21', n_{11}, o_{10}, p_{10}, q_{10}, r_{10}, s_{10}
  388. Mirror(V_6, e) → T_9
  389. Mirror(W_6, e) → U_9
  390. Mirror(Z_6, e) → V_9
  391. Mirror(A_7, e) → W_9
  392. Mirror(B_7, e) → Z_9
  393. Mirror(C_7, e) → A_{10}
  394. Polygon(T_9, U_9, V_9, W_9, Z_9, A_{10}) → poly25, t_{10}, u_{10}, v_{14}, w_9, z_{10}, a_{18}
  395. Sequence(Sequence[Translate[{poly20, poly20', poly20'', poly20''', poly21, poly20'_1, poly22', poly20'''_1, poly22, poly23, poly24, poly21', poly24', poly25, poly20'''_2, poly20''_1}, Vector[((i * 4) * w_1) + ((4 * j) * v)]], i, (-n), n], j, (-n), n) → list12
  396. Rotate(C, 120*°, A) → C'_{15}
  397. Mirror(A, Line[C, C'_{15}]) → A_t
  398. PointIn(Polygon[C'_{15}, A_t, A]) → R
  399. PointIn(Polygon[C, A_t, A]) → Q
  400. Rotate(R, 120*°, A_t) → D_{10}
  401. Rotate(Q, 120*°, A) → E_{10}
  402. Polygon(A, Q, C, D_{10}, A_t, R, C'_{15}, E_{10}) → poly26, a_{19}, c_{17}, c_{18}, d_{11}, a'_{14}, b_{11}, c'_{15}, e_{11}
  403. Rotate(A, 120*°, A) → A'_{15}
  404. Rotate(Q, 120*°, A) → F_{10}
  405. Rotate(C, 120*°, A) → C'_{16}
  406. Rotate(D_{10}, 120*°, A) → G_{10}
  407. Rotate(A_t, 120*°, A) → H_{10}
  408. Rotate(R, 120*°, A) → I_{10}
  409. Rotate(C'_{15}, 120*°, A) → J_{10}
  410. Rotate(E_{10}, 120*°, A) → K_{10}
  411. Polygon(A'_{15}, F_{10}, C'_{16}, G_{10}, H_{10}, I_{10}, J_{10}, K_{10}) → poly26', a'_{15}, f_{11}, c'_{16}, g_{11}, h_{11}, i_{11}, j_{10}, k_{11}
  412. Rotate(A'_{15}, 120*°, A) → L_{10}
  413. Rotate(F_{10}, 120*°, A) → M_{10}
  414. Rotate(C'_{16}, 120*°, A) → N_{10}
  415. Rotate(G_{10}, 120*°, A) → O_{10}
  416. Rotate(H_{10}, 120*°, A) → P_{10}
  417. Rotate(I_{10}, 120*°, A) → Q_{10}
  418. Rotate(J_{10}, 120*°, A) → R_{10}
  419. Rotate(K_{10}, 120*°, A) → S_{10}
  420. Polygon(L_{10}, M_{10}, N_{10}, O_{10}, P_{10}, Q_{10}, R_{10}, S_{10}) → poly26'', l_{11}, m_{14}, n_{12}, o_{11}, p_{11}, q_{11}, r_{11}, s_{11}
  421. Rotate(A, 120*°, A_t) → A'_{16}
  422. Rotate(Q, 120*°, A_t) → T_{10}
  423. Rotate(C, 120*°, A_t) → C'_{17}
  424. Rotate(D_{10}, 120*°, A_t) → U_{10}
  425. Rotate(A_t, 120*°, A_t) → V_{10}
  426. Rotate(R, 120*°, A_t) → W_{10}
  427. Rotate(C'_{15}, 120*°, A_t) → Z_{10}
  428. Rotate(E_{10}, 120*°, A_t) → A_{11}
  429. Rotate(A'_{16}, 120*°, A_t) → B_{11}
  430. Rotate(T_{10}, 120*°, A_t) → C_{11}
  431. Rotate(C'_{17}, 120*°, A_t) → D_{11}
  432. Rotate(U_{10}, 120*°, A_t) → E_{11}
  433. Rotate(V_{10}, 120*°, A_t) → F_{11}
  434. Rotate(W_{10}, 120*°, A_t) → G_{11}
  435. Rotate(Z_{10}, 120*°, A_t) → H_{11}
  436. Rotate(A_{11}, 120*°, A_t) → I_{11}
  437. Vector(R, O_{10}) → w_{10}
  438. Rotate(w_{10}, 120*°) → u_{11}
  439. Sequence(Sequence[Translate[{poly26, poly26', poly26''}, Vector[(i * w_{10}) + (j * u_{11})]], i, (-n), n], j, (-n), n) → list13
  440. Polygon(A, I - h, C, J_{11}, I, G, H) → poly28, j_{11}, e_{13}, f_{13}, c_{19}, a_{21}, h_{23}, j_{23}
  441. Polygon(A, H, G) → poly27, e_{12}, a_{20}, f_{12}
  442. Mirror(A, l) → A'_{17}
  443. Mirror(C, l) → C'_{18}
  444. Mirror(J_{11}, l) → K_{11}
  445. Mirror(G, l) → E'_1
  446. Mirror(H, l) → F'_4
  447. Mirror(poly28, l) → poly28'
  448. Mirror(A, l) → A'_{18}
  449. Mirror(H, l) → F'_5
  450. Mirror(G, l) → E'_2
  451. Polygon(A'_{18}, F'_5, E'_2) → poly27', e'_2, a'_{18}, f'_5
  452. Sequence(Sequence[Translate[{poly27, poly27', poly28, poly28'}, Vector[(i * h) + ((j * 2) * v)]], i, (-n), n], j, (-n), n) → list3
  453. PointIn(Polygon[A, C, A_t]) → S
  454. Polygon(A, S, C) → poly29, c_{20}, a_{22}, l_{12}
  455. Polygon(A, A_t, C, S) → poly30, a_{23}, a_t, c_{21}, l_{13}
  456. Line(A_t, C) → t_{11}
  457. Mirror(A, t_{11}) → A'_{14}
  458. Mirror(A_t, t_{11}) → M_{11}
  459. Mirror(C, t_{11}) → C'_{19}
  460. Mirror(S, t_{11}) → N_{11}
  461. Polygon(A'_{14}, M_{11}, C'_{19}, N_{11}) → poly30', a'_1, m_{15}, c'_{19}, n_{13}
  462. Mirror(A, t_{11}) → A'_{19}
  463. Mirror(S, t_{11}) → O_{11}
  464. Mirror(C, t_{11}) → C'_{20}
  465. Polygon(A'_{19}, O_{11}, C'_{20}) → poly29', c'_{20}, a'_{19}, o_{12}
  466. Rotate(A, 120*°, A_t) → A'_{20}
  467. Rotate(A_t, 120*°, A_t) → P_{11}
  468. Rotate(C, 120*°, A_t) → C'_{21}
  469. Rotate(S, 120*°, A_t) → Q_{11}
  470. Polygon(A'_{20}, P_{11}, C'_{21}, Q_{11}) → poly30'_1, a'_{20}, p_{12}, c'_{21}, q_{12}
  471. Rotate(A, 120*°, A_t) → A'_{21}
  472. Rotate(S, 120*°, A_t) → R_{11}
  473. Rotate(C, 120*°, A_t) → C'_{22}
  474. Polygon(A'_{21}, R_{11}, C'_{22}) → poly29'_1, c'_{22}, a'_{21}, r_{12}
  475. Rotate(A'_{19}, 120*°, A_t) → S_{11}
  476. Rotate(O_{11}, 120*°, A_t) → T_{11}
  477. Rotate(C'_{20}, 120*°, A_t) → U_{11}
  478. Polygon(S_{11}, T_{11}, U_{11}) → poly29'', u_{12}, s_{12}, t_{12}
  479. Rotate(A'_{14}, 120*°, A_t) → V_{11}
  480. Rotate(M_{11}, 120*°, A_t) → W_{11}
  481. Rotate(C'_{19}, 120*°, A_t) → Z_{11}
  482. Rotate(N_{11}, 120*°, A_t) → A_{12}
  483. Polygon(V_{11}, W_{11}, Z_{11}, A_{12}) → poly30'', v_{15}, w_{11}, z_{11}, a_{24}
  484. Rotate(A'_{20}, 120*°, A_t) → B_{12}
  485. Rotate(P_{11}, 120*°, A_t) → C_{12}
  486. Rotate(C'_{21}, 120*°, A_t) → D_{12}
  487. Rotate(Q_{11}, 120*°, A_t) → E_{12}
  488. Polygon(B_{12}, C_{12}, D_{12}, E_{12}) → poly31, b_{12}, c_{22}, d_{12}, e_{14}
  489. Rotate(A'_{21}, 120*°, A_t) → F_{12}
  490. Rotate(R_{11}, 120*°, A_t) → G_{12}
  491. Rotate(C'_{22}, 120*°, A_t) → H_{12}
  492. Polygon(F_{12}, G_{12}, H_{12}) → poly32, h_{12}, f_{14}, g_{12}
  493. Rotate(S_{11}, 120*°, A_t) → I_{12}
  494. Rotate(T_{11}, 120*°, A_t) → J_{12}
  495. Rotate(U_{11}, 120*°, A_t) → K_{12}
  496. Polygon(I_{12}, J_{12}, K_{12}) → poly29''', k_{13}, i_{12}, j_{12}
  497. Rotate(V_{11}, 120*°, A_t) → L_{12}
  498. Rotate(W_{11}, 120*°, A_t) → M_{12}
  499. Rotate(Z_{11}, 120*°, A_t) → N_{12}
  500. Rotate(A_{12}, 120*°, A_t) → O_{12}
  501. Polygon(L_{12}, M_{12}, N_{12}, O_{12}) → poly30''', l_{14}, m_{16}, n_{14}, o_{13}
  502. Sequence(Sequence[Translate[{poly29, poly29', poly29'', poly29''', poly32, poly29'_1, poly30, poly30', poly30'', poly30''', poly30'_1, poly31}, Vector[(i * u_{11}) + (j * w_{10})]], i, (-n), n], j, (-n), n) → list14
  503. Midpoint(Intersect[e, OrthogonalLine[A_t, e]], A_t) → L_{11}
  504. Line(L_{11}, e) → b_{13}
  505. PointIn(Polygon[C, A, A_t]) → T
  506. Rotate(T, 120*°, B_{10}) → Q_{12}
  507. Rotate(Q_{12}, 120*°, B_{10}) → R_{12}
  508. Polygon(A, C, T, B_{10}, R_{12}) → poly33, a_{25}, c_{23}, p_{13}, b_{14}, r_{13}
  509. Rotate(A, 120*°, B_{10}) → A'_{22}
  510. Rotate(C, 120*°, B_{10}) → C'_{23}
  511. Rotate(T, 120*°, B_{10}) → S_{12}
  512. Rotate(B_{10}, 120*°, B_{10}) → T_{12}
  513. Rotate(R_{12}, 120*°, B_{10}) → U_{12}
  514. Polygon(A'_{22}, C'_{23}, S_{12}, T_{12}, U_{12}) → poly33', a'_{22}, c'_{23}, s_{13}, t_{13}, u_{13}
  515. Rotate(A'_{22}, 120*°, B_{10}) → V_{12}
  516. Rotate(C'_{23}, 120*°, B_{10}) → W_{12}
  517. Rotate(S_{12}, 120*°, B_{10}) → Z_{12}
  518. Rotate(T_{12}, 120*°, B_{10}) → A_{13}
  519. Rotate(U_{12}, 120*°, B_{10}) → B_{13}
  520. Polygon(V_{12}, W_{12}, Z_{12}, A_{13}, B_{13}) → poly33'', v_{16}, w_{12}, z_{12}, a_{26}, b_{15}
  521. Mirror(A'_{22}, t_{11}) → C_{13}
  522. Mirror(C'_{23}, t_{11}) → D_{13}
  523. Mirror(S_{12}, t_{11}) → E_{13}
  524. Mirror(T_{12}, t_{11}) → F_{13}
  525. Mirror(U_{12}, t_{11}) → G_{13}
  526. Polygon(C_{13}, D_{13}, E_{13}, F_{13}, G_{13}) → poly33''_1, c_{24}, d_{13}, e_{15}, f_{15}, g_{13}
  527. Mirror(V_{12}, t_{11}) → H_{13}
  528. Mirror(W_{12}, t_{11}) → I_{13}
  529. Mirror(Z_{12}, t_{11}) → J_{13}
  530. Mirror(A_{13}, t_{11}) → K_{13}
  531. Mirror(B_{13}, t_{11}) → N_{13}
  532. Polygon(H_{13}, I_{13}, J_{13}, K_{13}, N_{13}) → poly33''', h_{13}, i_{13}, j_{13}, k_{14}, n_{15}
  533. Mirror(A, t_{11}) → A'_{23}
  534. Mirror(C, t_{11}) → C'_{24}
  535. Mirror(T, t_{11}) → O_{13}
  536. Mirror(B_{10}, t_{11}) → P_{13}
  537. Mirror(R_{12}, t_{11}) → Q_{13}
  538. Polygon(A'_{23}, C'_{24}, O_{13}, P_{13}, Q_{13}) → poly33'_1, a'_{23}, c'_{24}, o_{14}, p_{14}, q_{13}
  539. Rotate(V_{12}, 120*°, A_t) → R_{13}
  540. Rotate(W_{12}, 120*°, A_t) → S_{13}
  541. Rotate(Z_{12}, 120*°, A_t) → T_{13}
  542. Rotate(A_{13}, 120*°, A_t) → U_{13}
  543. Rotate(B_{13}, 120*°, A_t) → V_{13}
  544. Polygon(R_{13}, S_{13}, T_{13}, U_{13}, V_{13}) → poly33'''_1, r_{14}, s_{14}, t_{14}, u_{14}, v_{17}
  545. Rotate(A, 120*°, A_t) → A'_{24}
  546. Rotate(C, 120*°, A_t) → C'_{25}
  547. Rotate(T, 120*°, A_t) → W_{13}
  548. Rotate(B_{10}, 120*°, A_t) → Z_{13}
  549. Rotate(R_{12}, 120*°, A_t) → A_{14}
  550. Polygon(A'_{24}, C'_{25}, W_{13}, Z_{13}, A_{14}) → poly33'_2, a'_{24}, c'_{25}, w_{13}, z_{13}, a_{27}
  551. Rotate(A'_{22}, 120*°, A_t) → B_{14}
  552. Rotate(C'_{23}, 120*°, A_t) → C_{14}
  553. Rotate(S_{12}, 120*°, A_t) → D_{14}
  554. Rotate(T_{12}, 120*°, A_t) → E_{14}
  555. Rotate(U_{12}, 120*°, A_t) → F_{14}
  556. Polygon(B_{14}, C_{14}, D_{14}, E_{14}, F_{14}) → poly33''_2, b_{16}, c_{25}, d_{14}, e_{16}, f_{16}
  557. Rotate(C_{13}, 120*°, A_t) → G_{14}
  558. Rotate(D_{13}, 120*°, A_t) → H_{14}
  559. Rotate(E_{13}, 120*°, A_t) → I_{14}
  560. Rotate(F_{13}, 120*°, A_t) → J_{14}
  561. Rotate(G_{13}, 120*°, A_t) → K_{14}
  562. Polygon(G_{14}, H_{14}, I_{14}, J_{14}, K_{14}) → poly34, g_{14}, h_{14}, i_{14}, j_{14}, k_{15}
  563. Rotate(H_{13}, 120*°, A_t) → L_{14}
  564. Rotate(I_{13}, 120*°, A_t) → M_{14}
  565. Rotate(J_{13}, 120*°, A_t) → N_{14}
  566. Rotate(K_{13}, 120*°, A_t) → O_{14}
  567. Rotate(N_{13}, 120*°, A_t) → P_{14}
  568. Polygon(L_{14}, M_{14}, N_{14}, O_{14}, P_{14}) → poly35, l_{15}, m_{17}, n_{16}, o_{15}, p_{15}
  569. Rotate(A'_{23}, 120*°, A_t) → Q_{14}
  570. Rotate(C'_{24}, 120*°, A_t) → R_{14}
  571. Rotate(O_{13}, 120*°, A_t) → S_{14}
  572. Rotate(P_{13}, 120*°, A_t) → T_{14}
  573. Rotate(Q_{13}, 120*°, A_t) → U_{14}
  574. Polygon(Q_{14}, R_{14}, S_{14}, T_{14}, U_{14}) → poly36, q_{14}, r_{15}, s_{15}, t_{15}, u_{15}
  575. Rotate(A'_{24}, 120*°, A_t) → V_{14}
  576. Rotate(C'_{25}, 120*°, A_t) → W_{14}
  577. Rotate(W_{13}, 120*°, A_t) → Z_{14}
  578. Rotate(Z_{13}, 120*°, A_t) → A_{15}
  579. Rotate(A_{14}, 120*°, A_t) → B_{15}
  580. Polygon(V_{14}, W_{14}, Z_{14}, A_{15}, B_{15}) → poly37, v_{18}, w_{14}, z_{14}, a_{28}, b_{17}
  581. Rotate(R_{13}, 120*°, A_t) → C_{15}
  582. Rotate(S_{13}, 120*°, A_t) → D_{15}
  583. Rotate(T_{13}, 120*°, A_t) → E_{15}
  584. Rotate(U_{13}, 120*°, A_t) → F_{15}
  585. Rotate(V_{13}, 120*°, A_t) → G_{15}
  586. Polygon(C_{15}, D_{15}, E_{15}, F_{15}, G_{15}) → poly38, c_{26}, d_{15}, e_{17}, f_{17}, g_{15}
  587. Rotate(B_{14}, 120*°, A_t) → H_{15}
  588. Rotate(C_{14}, 120*°, A_t) → I_{15}
  589. Rotate(D_{14}, 120*°, A_t) → J_{15}
  590. Rotate(E_{14}, 120*°, A_t) → K_{15}
  591. Rotate(F_{14}, 120*°, A_t) → L_{15}
  592. Polygon(H_{15}, I_{15}, J_{15}, K_{15}, L_{15}) → poly39, h_{15}, i_{15}, j_{15}, k_{16}, l_{16}
  593. Rotate(Q_{14}, 120*°, A_t) → M_{15}
  594. Rotate(R_{14}, 120*°, A_t) → N_{15}
  595. Rotate(S_{14}, 120*°, A_t) → O_{15}
  596. Rotate(T_{14}, 120*°, A_t) → P_{15}
  597. Rotate(U_{14}, 120*°, A_t) → Q_{15}
  598. Polygon(M_{15}, N_{15}, O_{15}, P_{15}, Q_{15}) → poly36', m_{18}, n_{17}, o_{16}, p_{16}, q_{15}
  599. Rotate(L_{14}, 120*°, A_t) → R_{15}
  600. Rotate(M_{14}, 120*°, A_t) → S_{15}
  601. Rotate(N_{14}, 120*°, A_t) → T_{15}
  602. Rotate(O_{14}, 120*°, A_t) → U_{15}
  603. Rotate(P_{14}, 120*°, A_t) → V_{15}
  604. Polygon(R_{15}, S_{15}, T_{15}, U_{15}, V_{15}) → poly35', r_{16}, s_{16}, t_{16}, u_{16}, v_{19}
  605. Rotate(G_{14}, 120*°, A_t) → W_{15}
  606. Rotate(H_{14}, 120*°, A_t) → Z_{15}
  607. Rotate(I_{14}, 120*°, A_t) → A_{16}
  608. Rotate(J_{14}, 120*°, A_t) → B_{16}
  609. Rotate(K_{14}, 120*°, A_t) → C_{16}
  610. Polygon(W_{15}, Z_{15}, A_{16}, B_{16}, C_{16}) → poly34', w_{15}, z_{15}, a_{29}, b_{18}, c_{27}
  611. Sequence(Sequence[Translate[{poly33, poly33'_1, poly33'_2, poly36, poly36', poly33', poly33''_1, poly33''_2, poly34, poly39, poly34', poly33'', poly33''', poly33'''_1, poly35, poly38, poly35', poly37}, Vector[(i * u_{11}) + (j * w_{10})]], i, (-n), n], j, (-n), n) → list15
  612. Midpoint(A_t, C) → P_{12}
  613. Rotate(A'_{22}, 180*°, P_{12}) → D_{16}
  614. Rotate(C'_{23}, 180*°, P_{12}) → E_{16}
  615. Rotate(S_{12}, 180*°, P_{12}) → F_{16}
  616. Rotate(T_{12}, 180*°, P_{12}) → G_{16}
  617. Rotate(U_{12}, 180*°, P_{12}) → H_{16}
  618. Polygon(D_{16}, E_{16}, F_{16}, G_{16}, H_{16}) → poly33''_3, d_{16}, e_{18}, f_{18}, g_{16}, h_{16}
  619. Rotate(A, 180*°, P_{12}) → A'_{25}
  620. Rotate(C, 180*°, P_{12}) → C'_{26}
  621. Rotate(T, 180*°, P_{12}) → N'_1
  622. Rotate(B_{10}, 180*°, P_{12}) → I_{16}
  623. Rotate(R_{12}, 180*°, P_{12}) → J_{16}
  624. Polygon(A'_{25}, C'_{26}, N'_1, I_{16}, J_{16}) → poly33'_3, a'_{25}, c'_{26}, n'_1, i_{16}, j_{16}
  625. Rotate(V_{12}, 180*°, P_{12}) → K_{16}
  626. Rotate(W_{12}, 180*°, P_{12}) → L_{16}
  627. Rotate(Z_{12}, 180*°, P_{12}) → M_{16}
  628. Rotate(A_{13}, 180*°, P_{12}) → O_{16}
  629. Rotate(B_{13}, 180*°, P_{12}) → P_{16}
  630. Polygon(K_{16}, L_{16}, M_{16}, O_{16}, P_{16}) → poly33'''_2, k_{17}, l_{17}, m_{19}, o_{17}, p_{17}
  631. Rotate(P_{12}, 60*°, A_t) → Q_{16}
  632. Rotate(P_{12}, 120*°, A_t) → R_{16}
  633. Rotate(P_{12}, 180*°, A_t) → S_{16}
  634. Rotate(P_{12}, 240*°, A_t) → T_{16}
  635. Rotate(A'_{25}, 180*°, Q_{16}) → U_{16}
  636. Rotate(C'_{26}, 180*°, Q_{16}) → V_{16}
  637. Rotate(N'_1, 180*°, Q_{16}) → W_{16}
  638. Rotate(I_{16}, 180*°, Q_{16}) → Z_{16}
  639. Rotate(J_{16}, 180*°, Q_{16}) → A_{17}
  640. Polygon(U_{16}, V_{16}, W_{16}, Z_{16}, A_{17}) → poly40, u_{17}, v_{20}, w_{16}, z_{16}, a_{30}
  641. Rotate(K_{16}, 180*°, Q_{16}) → B_{17}
  642. Rotate(L_{16}, 180*°, Q_{16}) → C_{17}
  643. Rotate(M_{16}, 180*°, Q_{16}) → D_{17}
  644. Rotate(O_{16}, 180*°, Q_{16}) → E_{17}
  645. Rotate(P_{16}, 180*°, Q_{16}) → F_{17}
  646. Polygon(B_{17}, C_{17}, D_{17}, E_{17}, F_{17}) → poly41, b_{19}, c_{28}, d_{17}, e_{19}, f_{19}
  647. Rotate(D_{16}, 180*°, Q_{16}) → G_{17}
  648. Rotate(E_{16}, 180*°, Q_{16}) → H_{17}
  649. Rotate(F_{16}, 180*°, Q_{16}) → I_{17}
  650. Rotate(G_{16}, 180*°, Q_{16}) → J_{17}
  651. Rotate(H_{16}, 180*°, Q_{16}) → K_{17}
  652. Polygon(G_{17}, H_{17}, I_{17}, J_{17}, K_{17}) → poly42, g_{17}, h_{17}, i_{17}, j_{17}, k_{18}
  653. Rotate(B_{17}, 180*°, R_{16}) → L_{17}
  654. Rotate(C_{17}, 180*°, R_{16}) → M_{17}
  655. Rotate(D_{17}, 180*°, R_{16}) → N_{17}
  656. Rotate(E_{17}, 180*°, R_{16}) → O_{17}
  657. Rotate(F_{17}, 180*°, R_{16}) → P_{17}
  658. Polygon(L_{17}, M_{17}, N_{17}, O_{17}, P_{17}) → poly41', l_{18}, m_{20}, n_{18}, o_{18}, p_{18}
  659. Rotate(G_{17}, 180*°, R_{16}) → Q_{17}
  660. Rotate(H_{17}, 180*°, R_{16}) → R_{17}
  661. Rotate(I_{17}, 180*°, R_{16}) → S_{17}
  662. Rotate(J_{17}, 180*°, R_{16}) → T_{17}
  663. Rotate(K_{17}, 180*°, R_{16}) → U_{17}
  664. Polygon(Q_{17}, R_{17}, S_{17}, T_{17}, U_{17}) → poly42', q_{17}, r_{17}, s_{17}, t_{17}, u_{18}
  665. Rotate(U_{16}, 180*°, R_{16}) → V_{17}
  666. Rotate(V_{16}, 180*°, R_{16}) → W_{17}
  667. Rotate(W_{16}, 180*°, R_{16}) → Z_{17}
  668. Rotate(Z_{16}, 180*°, R_{16}) → A_{18}
  669. Rotate(A_{17}, 180*°, R_{16}) → B_{18}
  670. Polygon(V_{17}, W_{17}, Z_{17}, A_{18}, B_{18}) → poly40', v_{21}, w_{17}, z_{17}, a_{31}, b_{20}
  671. Rotate(Q_{17}, 180*°, S_{16}) → C_{18}
  672. Rotate(R_{17}, 180*°, S_{16}) → D_{18}
  673. Rotate(S_{17}, 180*°, S_{16}) → E_{18}
  674. Rotate(T_{17}, 180*°, S_{16}) → F_{18}
  675. Rotate(U_{17}, 180*°, S_{16}) → G_{18}
  676. Polygon(C_{18}, D_{18}, E_{18}, F_{18}, G_{18}) → poly42'', c_{29}, d_{18}, e_{20}, f_{20}, g_{18}
  677. Rotate(V_{17}, 180*°, S_{16}) → H_{18}
  678. Rotate(W_{17}, 180*°, S_{16}) → I_{18}
  679. Rotate(Z_{17}, 180*°, S_{16}) → J_{18}
  680. Rotate(A_{18}, 180*°, S_{16}) → K_{18}
  681. Rotate(B_{18}, 180*°, S_{16}) → L_{18}
  682. Polygon(H_{18}, I_{18}, J_{18}, K_{18}, L_{18}) → poly40'', h_{18}, i_{18}, j_{18}, k_{19}, l_{19}
  683. Rotate(L_{17}, 180*°, S_{16}) → M_{18}
  684. Rotate(M_{17}, 180*°, S_{16}) → N_{18}
  685. Rotate(N_{17}, 180*°, S_{16}) → O_{18}
  686. Rotate(O_{17}, 180*°, S_{16}) → P_{18}
  687. Rotate(P_{17}, 180*°, S_{16}) → Q_{18}
  688. Polygon(M_{18}, N_{18}, O_{18}, P_{18}, Q_{18}) → poly41'', m_{21}, n_{19}, o_{19}, p_{19}, q_{18}
  689. Rotate(H_{18}, 180*°, T_{16}) → R_{18}
  690. Rotate(I_{18}, 180*°, T_{16}) → S_{18}
  691. Rotate(J_{18}, 180*°, T_{16}) → T_{18}
  692. Rotate(K_{18}, 180*°, T_{16}) → U_{18}
  693. Rotate(L_{18}, 180*°, T_{16}) → V_{18}
  694. Polygon(R_{18}, S_{18}, T_{18}, U_{18}, V_{18}) → poly40''', r_{18}, s_{18}, t_{18}, u_{19}, v_{22}
  695. Rotate(C_{18}, 180*°, T_{16}) → W_{18}
  696. Rotate(D_{18}, 180*°, T_{16}) → Z_{18}
  697. Rotate(E_{18}, 180*°, T_{16}) → A_{19}
  698. Rotate(F_{18}, 180*°, T_{16}) → B_{19}
  699. Rotate(G_{18}, 180*°, T_{16}) → C_{19}
  700. Polygon(W_{18}, Z_{18}, A_{19}, B_{19}, C_{19}) → poly42''', w_{18}, z_{18}, a_{32}, b_{21}, c_{30}
  701. Rotate(M_{18}, 180*°, T_{16}) → D_{19}
  702. Rotate(N_{18}, 180*°, T_{16}) → E_{19}
  703. Rotate(O_{18}, 180*°, T_{16}) → F_{19}
  704. Rotate(P_{18}, 180*°, T_{16}) → G_{19}
  705. Rotate(Q_{18}, 180*°, T_{16}) → H_{19}
  706. Polygon(D_{19}, E_{19}, F_{19}, G_{19}, H_{19}) → poly41''', d_{19}, e_{21}, f_{21}, g_{19}, h_{19}
  707. Sequence(Sequence[Translate[{poly33, poly33'_3, poly40, poly40', poly40'', poly40''', poly33', poly33''_3, poly42, poly42', poly42'', poly42''', poly33'', poly33'''_2, poly41, poly41', poly41'', poly41'''}, Vector[(i * u_{11}) + (j * w_{10})]], i, (-n), n], j, (-n), n) → list16
  708. Intersect(d_5, Rotate[e, -30*°, C]) → I_{19}
  709. PointIn(Polygon[A, C, I_{19}]) → V
  710. Polygon(A, V, I_{19}) → poly43, i_{19}, a_{33}, j_{19}
  711. Polygon(C, I_{19}, V, A) → poly44, c_{31}, i_{20}, j_{20}, a_{34}
  712. Line(C, I_{19}) → q_{16}
  713. Mirror(C, q_{16}) → C'_{27}
  714. Mirror(I_{19}, q_{16}) → K_{19}
  715. Mirror(V, q_{16}) → L_{19}
  716. Mirror(A, q_{16}) → A'_{26}
  717. Polygon(C'_{27}, K_{19}, L_{19}, A'_{26}) → poly44', c'_{27}, k_{20}, l_{20}, a'_{26}
  718. Mirror(A, q_{16}) → A'_{27}
  719. Mirror(V, q_{16}) → M_{19}
  720. Mirror(I_{19}, q_{16}) → N_{19}
  721. Polygon(A'_{27}, M_{19}, N_{19}) → poly43', n_{20}, a'_{27}, m_{22}
  722. Mirror(C'_{27}, a'_{26}) → O_{19}
  723. Mirror(K_{19}, a'_{26}) → P_{19}
  724. Mirror(L_{19}, a'_{26}) → Q_{19}
  725. Mirror(A'_{26}, a'_{26}) → R_{19}
  726. Polygon(O_{19}, P_{19}, Q_{19}, R_{19}) → poly44'', o_{20}, p_{20}, q_{19}, r_{19}
  727. Mirror(A'_{27}, a'_{26}) → S_{19}
  728. Mirror(M_{19}, a'_{26}) → T_{19}
  729. Mirror(N_{19}, a'_{26}) → U_{19}
  730. Polygon(S_{19}, T_{19}, U_{19}) → poly43'', u_{20}, s_{19}, t_{19}
  731. Mirror(O_{19}, o_{20}) → V_{19}
  732. Mirror(P_{19}, o_{20}) → W_{19}
  733. Mirror(Q_{19}, o_{20}) → Z_{19}
  734. Mirror(R_{19}, o_{20}) → A_{20}
  735. Polygon(V_{19}, W_{19}, Z_{19}, A_{20}) → poly44''', v_{23}, w_{19}, z_{19}, a_{35}
  736. Mirror(S_{19}, o_{20}) → B_{20}
  737. Mirror(T_{19}, o_{20}) → C_{20}
  738. Mirror(U_{19}, o_{20}) → D_{20}
  739. Polygon(B_{20}, C_{20}, D_{20}) → poly43''', d_{20}, b_{22}, c_{32}
  740. Mirror(V_{19}, a_{35}) → E_{20}
  741. Mirror(W_{19}, a_{35}) → F_{20}
  742. Mirror(Z_{19}, a_{35}) → G_{20}
  743. Mirror(A_{20}, a_{35}) → H_{20}
  744. Polygon(E_{20}, F_{20}, G_{20}, H_{20}) → poly45, e_{22}, f_{22}, g_{20}, h_{20}
  745. Mirror(B_{20}, a_{35}) → I_{20}
  746. Mirror(C_{20}, a_{35}) → J_{20}
  747. Mirror(D_{20}, a_{35}) → K_{20}
  748. Polygon(I_{20}, J_{20}, K_{20}) → poly46, k_{21}, i_{21}, j_{21}
  749. Mirror(E_{20}, e_{22}) → L_{20}
  750. Mirror(F_{20}, e_{22}) → M_{20}
  751. Mirror(G_{20}, e_{22}) → N_{20}
  752. Mirror(H_{20}, e_{22}) → O_{20}
  753. Polygon(L_{20}, M_{20}, N_{20}, O_{20}) → poly45', l_{21}, m_{23}, n_{21}, o_{21}
  754. Mirror(I_{20}, e_{22}) → P_{20}
  755. Mirror(J_{20}, e_{22}) → Q_{20}
  756. Mirror(K_{20}, e_{22}) → R_{20}
  757. Polygon(P_{20}, Q_{20}, R_{20}) → poly46', r_{20}, p_{21}, q_{20}
  758. Mirror(P_{20}, e) → S_{20}
  759. Mirror(Q_{20}, e) → T_{20}
  760. Mirror(R_{20}, e) → U_{20}
  761. Polygon(S_{20}, T_{20}, U_{20}) → poly46'', u_{21}, s_{20}, t_{20}
  762. Mirror(L_{20}, e) → V_{20}
  763. Mirror(M_{20}, e) → W_{20}
  764. Mirror(N_{20}, e) → Z_{20}
  765. Mirror(O_{20}, e) → A_{21}
  766. Polygon(V_{20}, W_{20}, Z_{20}, A_{21}) → poly45'', v_{24}, w_{20}, z_{20}, a_{36}
  767. Mirror(I_{20}, e) → B_{21}
  768. Mirror(J_{20}, e) → C_{21}
  769. Mirror(K_{20}, e) → D_{21}
  770. Polygon(B_{21}, C_{21}, D_{21}) → poly46'_1, d_{21}, b_{23}, c_{33}
  771. Mirror(E_{20}, e) → E_{21}
  772. Mirror(F_{20}, e) → F_{21}
  773. Mirror(G_{20}, e) → G_{21}
  774. Mirror(H_{20}, e) → H_{21}
  775. Polygon(E_{21}, F_{21}, G_{21}, H_{21}) → poly45'_1, e_{23}, f_{23}, g_{21}, h_{21}
  776. Mirror(B_{20}, e) → I_{21}
  777. Mirror(C_{20}, e) → J_{21}
  778. Mirror(D_{20}, e) → K_{21}
  779. Polygon(I_{21}, J_{21}, K_{21}) → poly47, k_{22}, i_{22}, j_{22}
  780. Mirror(V_{19}, e) → L_{21}
  781. Mirror(W_{19}, e) → M_{21}
  782. Mirror(Z_{19}, e) → N_{21}
  783. Mirror(A_{20}, e) → O_{21}
  784. Polygon(L_{21}, M_{21}, N_{21}, O_{21}) → poly48, l_{22}, m_{24}, n_{22}, o_{22}
  785. Mirror(S_{19}, e) → P_{21}
  786. Mirror(T_{19}, e) → Q_{21}
  787. Mirror(U_{19}, e) → R_{21}
  788. Polygon(P_{21}, Q_{21}, R_{21}) → poly43'''_1, r_{21}, p_{22}, q_{21}
  789. Mirror(O_{19}, e) → S_{21}
  790. Mirror(P_{19}, e) → T_{21}
  791. Mirror(Q_{19}, e) → U_{21}
  792. Mirror(R_{19}, e) → V_{21}
  793. Polygon(S_{21}, T_{21}, U_{21}, V_{21}) → poly44'''_1, s_{21}, t_{21}, u_{22}, v_{25}
  794. Mirror(A'_{27}, e) → W_{21}
  795. Mirror(M_{19}, e) → Z_{21}
  796. Mirror(N_{19}, e) → A_{22}
  797. Polygon(W_{21}, Z_{21}, A_{22}) → poly43''_1, a_{37}, w_{21}, z_{21}
  798. Mirror(C'_{27}, e) → B_{22}
  799. Mirror(K_{19}, e) → C_{22}
  800. Mirror(L_{19}, e) → D_{22}
  801. Mirror(A'_{26}, e) → E_{22}
  802. Polygon(B_{22}, C_{22}, D_{22}, E_{22}) → poly44''_1, b_{24}, c_{34}, d_{22}, e_{24}
  803. Mirror(A, e) → A'_{28}
  804. Mirror(V, e) → F_{22}
  805. Mirror(I_{19}, e) → G_{22}
  806. Polygon(A'_{28}, F_{22}, G_{22}) → poly43'_1, g_{22}, a'_{28}, f_{24}
  807. Mirror(C, e) → C'_{28}
  808. Mirror(I_{19}, e) → H_{22}
  809. Mirror(V, e) → I_{22}
  810. Mirror(A, e) → A'_{29}
  811. Polygon(C'_{28}, H_{22}, I_{22}, A'_{29}) → poly44'_1, c'_{28}, h_{22}, i_{23}, a'_{29}
  812. Sequence(Sequence[Translate[{poly43, poly43', poly43'', poly43''', poly46, poly46', poly46'', poly46'_1, poly47, poly43'''_1, poly43''_1, poly43'_1, poly44, poly44', poly44'', poly44''', poly45, poly45', poly45'', poly45'_1, poly48, poly44'''_1, poly44''_1, poly44'_1}, Vector[((2 * i) * v) + (j * w_{22})]], i, (-n), n], j, (-n), n) → list17
  813. Sequence(Sequence[Translate[poly1, Vector[(i * u) + (j * v)]], i, (-n), n], j, (-n), n) → list1
  814. Polygon(A, H, G, I_{23}, K_5, C) → poly49, a_{38}, h_{24}, g_{24}, i_{24}, k_{24}, c_{35}
  815. Sequence(Sequence[Translate[{poly49, poly50, poly3', poly4'}, Vector[((i * 2) * h) + ((2 * j) * v)]], i, (-n), n], j, (-n), n) → list5

AI 绘图提示语参考

本提示语旨在绘制一个展示平面图案重复原理的示意图。图中应包含一条重复基准线、若干变换点以及由平移、反射和旋转生成的图案单元。构造顺序为:先绘制基准线,再确定变换点,然后通过平移、反射和旋转等几何变换生成不同图案,最后展示这些图案的重复关系。示意图需清晰体现17种 wallpaper groups 的基本概念,但避免具体命令或标签。
以上提示语为根据原始绘图命令整理而来,仅供参考。