Nakhchyvan Islamic Geometric Patterns

Nakhchyvan Islamic Geometric Patterns
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2019-12-31 22:02
This example demonstrates the construction of Islamic geometric patterns, focusing on symmetry, polygon creation, geometric transformations, and vector operations. It utilizes commands like Point, Rotate, Polygon, LineBisector, Distance, Ray, Intersect, Segment, Mirror, Vector, Translate, Centroid, Line, Sequence, Midpoint, OrthogonalLine, and Circle. Suitable for high school mathematics education or for enthusiasts exploring geometric constructions.

GeoGebra Commands & Parameters

  1. ConstructionStep() → stap
  2. Point(xAxis) → A
  3. Rotate(A, (360°) / 13) → A'
  4. Polygon(A, A', 13) → veelhoek1, f, p, q, j_1, k_1, B, C, D, E, F, G, g, H, I, J, C_1, D_1, h, i, j, k, l, m, n
  5. Point(xAxis) → K
  6. Rotate(L, (360°) / 13, K) → L'
  7. Polygon(L, L', 13) → veelhoek2, r, g_1, h_1, l_1, m_1, M, N, P, Q, R, S, s, T, U, V, E_1, F_1, t, a, b, c, d, e, f_1
  8. LineBisector(O, K) → vert
  9. Point(vert) → W
  10. Distance(A, A') → l11
  11. Rotate(A_1, rest7, Z) → B_1
  12. Ray(Z, B_1) → n_1
  13. Intersect(vert, n_1) → MM
  14. Polygon(Z, A_1, 11) → veelhoek3, p_1, e_1, f_2, G_1, H_1, I_1, J_1, K_1, L_1, M_1, N_1, q_1, O_1, r_1, s_1, t_1, a_1, b_1, c_1, d_1
  15. Rotate(A, ((-(360°))) / 26) → A'_1
  16. Rotate(A'_1, (-4 * (360°) / 13)) → P_1
  17. Segment(O, P_1) → g_2
  18. Rotate(W, ((-(360°))) / 11, MM) → W'
  19. Segment(MM, W') → h_2
  20. Mirror(veelhoek3, xAxis) → veelhoek3'
  21. Vector(Q_1, R_1) → u
  22. Translate(veelhoek2, u) → veelhoek2'
  23. Centroid(veelhoek2') → LO
  24. Mirror(veelhoek2', x = 4) → veelhoek2''
  25. Mirror(LO, x = 4) → RO
  26. Vector(S_1, T_1) → v
  27. Translate(veelhoek3, v) → veelhoek3'_1
  28. Centroid(veelhoek3'_1) → U_1
  29. Centroid(veelhoek3') → V_1
  30. Centroid(veelhoek2) → W_1
  31. Mirror(veelhoek3'_1, xAxis) → veelhoek4
  32. Centroid(veelhoek4) → Z_1
  33. Mirror(veelhoek4, x = 4) → veelhoek4'
  34. Centroid(veelhoek4') → A_2
  35. Mirror(veelhoek3'_1, x = 4) → veelhoek5
  36. Centroid(veelhoek5) → B_2
  37. Mirror(veelhoek2', xAxis) → veelhoek2''_1
  38. Centroid(veelhoek2''_1) → C_2
  39. Mirror(veelhoek2'', xAxis) → veelhoek2'''
  40. Centroid(veelhoek2''') → D_2
  41. Line(C_2, D_2) → i_1
  42. Line(LO, RO) → i_2
  43. Line(Z_1, U_1) → j_2
  44. Line(A_2, B_2) → k_2
  45. Intersect(i_1, j_2) → E_2
  46. Intersect(i_1, k_2) → F_2
  47. Intersect(i_2, k_2) → G_2
  48. Intersect(i_2, j_2) → H_2
  49. Polygon(E_2, H_2, G_2, F_2) → vierhoek1, e_2, l_2, m_2, n_2
  50. Sequence(Segment[Rotate[O, (nn * (360°) / 13)], Rotate[A, (nn * (360°) / 13)]], nn, 1, 13) → l1
  51. Midpoint(A, D_1) → I_2
  52. Sequence(Segment[Rotate[O, (nn * (360°) / 13)], Rotate[I_2, (nn * (360°) / 13)]], nn, 1, 13) → l2
  53. Mirror(l1, x = 4) → l1'
  54. Mirror(l2, x = 4) → l2'
  55. Translate(l1, Vector[O, RO]) → l1'_1
  56. Translate(l2, Vector[O, RO]) → l2'_1
  57. Translate(l1', Vector[W_1, LO]) → l1''
  58. Translate(l2', Vector[W_1, LO]) → l2''
  59. Translate(l1, Vector[O, D_2]) → l1'_2
  60. Translate(l2, Vector[O, D_2]) → l2'_2
  61. Translate(l1', Vector[W_1, C_2]) → l1''_1
  62. Translate(l2', Vector[W_1, C_2]) → l2''_1
  63. Sequence(Segment[Rotate[MM, (nn * (360°) / 11), MM], Rotate[K_1, (nn * (360°) / 11), MM]], nn, 1, 11) → l3
  64. Sequence(Segment[Rotate[MM, (nn * (360°) / 11), MM], Rotate[W, (nn * (360°) / 11), MM]], nn, 1, 11) → l4
  65. Translate(l3, Vector[MM, U_1]) → l3'
  66. Translate(l4, Vector[MM, U_1]) → l4'
  67. Translate(l4, Vector[MM, B_2]) → l4'_1
  68. Translate(l3, Vector[MM, B_2]) → l3'_1
  69. Mirror(l3, Line[C_2, O]) → l3'_2
  70. Mirror(l4, Line[C_2, O]) → l4'_2
  71. Mirror(l4, Line[D_2, W_1]) → l4'_3
  72. Mirror(l3, Line[D_2, W_1]) → l3'_3
  73. Mirror(l3, Line[O, W_1]) → l3'_4
  74. Mirror(l4, Line[O, W_1]) → l4'_4
  75. Translate(A, Vector[O, D_2]) → A'_2
  76. Rotate(A'_2, (360°) / 26, D_2) → J_2
  77. Rotate(K_1, ((-(360°))) / 22, MM) → K_2
  78. Ray(MM, K_2) → p_2
  79. Ray(D_2, J_2) → q_2
  80. Intersect(p_2, q_2) → L_2
  81. Intersect(vert, n_2) → M_2
  82. Mirror(L_2, vert) → N_2
  83. Rotate(H_1, h11 / 2, MM) → O_2
  84. Ray(MM, O_2) → r_2
  85. Translate(B, Vector[O, D_2]) → B'
  86. Rotate(B', (360°) / 26, D_2) → B''
  87. Ray(D_2, B'') → s_2
  88. Rotate(B', (3 * (360°) / 26), D_2) → B''_1
  89. Ray(D_2, B''_1) → b_2
  90. Rotate(M_1, (360°) / 22, MM) → Q_2
  91. Rotate(D, h11 / 2, V_1) → D'
  92. Translate(D', Vector[V_1, A_2]) → D''
  93. Ray(A_2, D'') → c_2
  94. Intersect(b_2, c_2) → R_2
  95. Segment(D_2, R_2) → d_2
  96. Segment(A_2, R_2) → f_3
  97. Rotate(H_1, ((-(360°))) / 22, MM) → S_2
  98. Ray(MM, S_2) → g_3
  99. Rotate(N, (360°) / 26, W_1) → N'
  100. Ray(K, N') → h_3
  101. Intersect(g_3, h_3) → T_2
  102. Segment(MM, T_2) → i_3
  103. Segment(K, T_2) → j_3
  104. Rotate(N, ((-(360°))) / 26, W_1) → N'_1
  105. Ray(K, N'_1) → k_3
  106. Segment(K, D_2) → l_3
  107. Mirror(T_2, l_3) → U_2
  108. Ray(MM, H_1) → m_3
  109. Intersect(l_3, m_3) → I_3
  110. Rotate(H_2, ((-(360°))) / 13, LO) → P_2
  111. Ray(LO, P_2) → t_2
  112. Rotate(H_2, (-2 * (360°) / 13), LO) → Z_2
  113. Point(l2'') → A_3
  114. Segment(U_1, W_2) → n_3
  115. Segment(W_2, LO) → q_3
  116. Segment(W_2, A_3) → s_3
  117. OrthogonalLine(A_3, s_3) → t_3
  118. Point(l2'') → B_3
  119. Circle(W_2, B_3) → c_3
  120. Point(e_2) → C_3
  121. Intersect(c_3, n_3, 1) → D_3
  122. Intersect(c_3, q_3, 1) → E_3
  123. OrthogonalLine(D_3, n_3) → p_3
  124. OrthogonalLine(E_3, q_3) → r_3
  125. Point(c_3) → F_3
  126. Rotate(W_2, (360°) / 13, LO) → V_2
  127. Segment(W_2, V_2) → a_2
  128. Intersect(c_3, a_2, 1) → G_3
  129. Ray(A_3, G_3) → a_3
  130. Intersect(e_2, a_3) → H_3
  131. Ray(W_2, F_3) → b_3
  132. OrthogonalLine(F_3, b_3) → d_3
  133. Intersect(p_3, d_3) → K_3
  134. Intersect(e_2, p_3) → L_3
  135. Intersect(r_3, a_3) → M_3
  136. Rotate(M_3, ((-(360°))) / 13, LO) → N_3
  137. Polygon(H_3, M_3, N_3, K_3, L_3) → veelhoek6, e_3, f_4, g_4, h_4, i_4
  138. Polygon(L_3, K_3, 11) → veelhoek7, j_4, t_4, a_4, O_3, P_3, Q_3, R_3, S_3, T_3, U_3, V_3, k_4, W_3, l_4, m_4, n_4, p_4, q_4, r_4, s_4
  139. Polygon(N_3, M_3, 13) → veelhoek8, b_4, k_5, l_5, m_5, n_5, Z_3, A_4, B_4, C_4, D_4, E_4, c_4, F_4, G_4, H_4, I_4, J_4, d_4, e_4, f_5, g_5, h_5, i_5, j_5
  140. Rotate(W_2, ((-(360°))) / 13, LO) → K_4
  141. Circle(K_4, F_3) → c_5
  142. Line(U_1, O_3) → p_5
  143. Rotate(H_2, (-3 * (360°) / 13), LO) → L_4
  144. Line(A_3, L_4) → q_5
  145. Intersect(q_5, p_5) → M_4
  146. Rotate(M_3, (-2 * (360°) / 13), LO) → N_4
  147. Polygon(N_3, N_4, M_4, O_3, K_3) → veelhoek9, r_5, s_5, t_5, o_3, a_5
  148. Polygon(H_2, Z_3, M_3, H_3) → vierhoek2, b_5, z_3, d_5, e_5
  149. Segment(A_3, O) → f_6
  150. Mirror(H_3, f_6) → O_4
  151. Mirror(K_3, f_6) → R_4
  152. Mirror(L_3, f_6) → S_4
  153. Mirror(M_4, f_6) → V_4
  154. Mirror(O_3, f_6) → W_4
  155. Mirror(K_3, f_6) → Z_4
  156. Midpoint(O, A_3) → A_5
  157. Polygon(N_4, I_4, V_4, A_5, M_4) → veelhoek10, g_6, h_6, v_4, i_6, j_6
  158. Polygon(I_4, H_4, R_4, W_4, V_4) → veelhoek11, k_6, l_6, m_6, w_4, n_6
  159. Polygon(G_4, O_4, S_4, R_4, H_4) → veelhoek12, p_6, o_4, q_6, r_6, s_6
  160. Midpoint(H_2, G_2) → P_4
  161. Mirror(O_4, l_2) → Q_4
  162. Polygon(G_4, F_4, Q_4, P_4, O_4) → veelhoek13, t_6, a_6, b_6, c_6, d_6
  163. Mirror(M_4, Line[U_1, A_5]) → T_4
  164. Polygon(O_3, M_4, A_5, T_4, P_3) → veelhoek14, e_6, f_7, g_7, h_7, i_7
  165. Polygon(W_4, R_4, 11) → veelhoek15, j_7, t_7, a_7, U_4, B_5, C_5, D_5, E_5, F_5, G_5, H_5, k_7, I_5, l_7, m_7, n_7, p_7, q_7, r_7, s_7
  166. Mirror(V_4, Line[V_1, A_5]) → J_5
  167. Polygon(A_5, V_4, W_4, I_5, J_5) → veelhoek16, b_7, c_7, d_7, e_7, f_8
  168. Mirror(veelhoek8, x = 4) → veelhoek8'
  169. Mirror(G_4, x = 4) → K_5
  170. Mirror(F_4, x = 4) → L_5
  171. Mirror(Q_4, x = 4) → M_5
  172. Mirror(P_4, x = 4) → N_5
  173. Mirror(O_4, x = 4) → O_5
  174. Polygon(K_5, L_5, M_5, N_5, O_5) → veelhoek13', g_8, h_8, i_8, j_8, o_5
  175. Polygon(B_5, S_4, O_4, N_5, O_5) → veelhoek17, k_8, l_8, m_8, n_8, p_8
  176. Mirror(G_4, x = 4) → P_5
  177. Mirror(O_4, x = 4) → Q_5
  178. Mirror(S_4, x = 4) → R_5
  179. Mirror(R_4, x = 4) → S_5
  180. Mirror(H_4, x = 4) → T_5
  181. Mirror(I_4, x = 4) → U_5
  182. Mirror(H_4, x = 4) → V_5
  183. Mirror(R_4, x = 4) → W_5
  184. Mirror(W_4, x = 4) → Z_5
  185. Mirror(V_4, x = 4) → A_6
  186. Polygon(K_5, T_5, C_5, B_5, O_5) → veelhoek18, q_8, r_8, s_8, t_8, a_8
  187. Polygon(C_5, T_5, U_5, A_6, D_5) → veelhoek19, b_8, c_8, u_5, d_8, e_8
  188. Mirror(A_5, x = 4) → B_6
  189. Mirror(V_4, x = 4) → C_6
  190. Mirror(W_4, x = 4) → D_6
  191. Mirror(I_5, x = 4) → E_6
  192. Mirror(J_5, x = 4) → F_6
  193. Polygon(D_5, A_6, B_6, F_6, E_5) → veelhoek20, f_9, g_9, h_9, i_9, j_9
  194. Mirror(N_4, x = 4) → G_6
  195. Mirror(I_4, x = 4) → H_6
  196. Mirror(V_4, x = 4) → I_6
  197. Mirror(A_5, x = 4) → J_6
  198. Mirror(M_4, x = 4) → K_6
  199. Polygon(G_6, H_6, I_6, J_6, K_6) → veelhoek10', k_9, l_9, m_9, n_9, p_9
  200. Mirror(O_3, x = 4) → L_6
  201. Mirror(K_3, x = 4) → M_6
  202. Mirror(N_3, x = 4) → O_6
  203. Polygon(G_6, O_6, M_6, L_6, K_6) → veelhoek21, q_9, o_6, r_9, s_9, t_9
  204. Mirror(N_3, x = 4) → N_6
  205. Polygon(L_6, M_6, 11) → veelhoek22, a_9, j_{10}, k_{10}, P_6, Q_6, R_6, S_6, T_6, U_6, V_6, W_6, b_9, Z_6, c_9, d_9, e_9, f_{10}, g_{10}, h_{10}, i_{10}
  206. Mirror(H_3, x = 4) → A_7
  207. Mirror(M_3, x = 4) → B_7
  208. Polygon(N_6, B_7, A_7, P_6, M_6) → veelhoek23, l_{10}, m_{10}, n_{10}, p_{10}, q_{10}
  209. Mirror(Z_3, x = 4) → C_7
  210. Polygon(C_7, G_2, A_7, B_7) → vierhoek3, r_{10}, s_{10}, t_{10}, a_{10}
  211. Circle(O, Distance[LO, G_4]) → c_{10}
  212. Rotate(C, ((-(360°))) / 26) → C'
  213. Ray(O, C') → b_{10}
  214. Intersect(c_{10}, b_{10}, 1) → D_7
  215. Rotate(D_7, (360°) / 13) → E_7
  216. Polygon(D_7, E_7, 13) → veelhoek24, d_{10}, m_{11}, n_{11}, p_{11}, q_{11}, F_7, G_7, H_7, I_7, J_7, K_7, e_{10}, L_7, M_7, N_7, O_7, P_7, f_{11}, g_{11}, h_{11}, i_{11}, j_{11}, k_{11}, l_{11}
  217. Polygon(D_7, T_4, A_5, J_5, E_7) → veelhoek25, r_{11}, s_{11}, t_{11}, a_{11}, b_{11}
  218. Polygon(P_7, Q_3, P_3, T_4, D_7) → veelhoek26, c_{11}, d_{11}, e_{11}, f_{12}, g_{12}
  219. Rotate(L_3, (5 * (360°) / 11), U_1) → Q_7
  220. Ray(U_1, Q_7) → h_{12}
  221. Ray(O, O_7) → i_{12}
  222. Intersect(h_{12}, i_{12}) → R_7
  223. Polygon(Q_7, Q_3, P_7, O_7, R_7) → veelhoek27, j_{12}, k_{12}, l_{12}, o_7, m_{12}
  224. Polygon(J_5, I_5, H_5, F_7, E_7) → veelhoek28, n_{12}, p_{12}, q_{12}, r_{12}, s_{12}
  225. Ray(O, G_7) → t_{12}
  226. Ray(V_1, G_5) → a_{12}
  227. Point(vert) → T_7
  228. Polygon(H_5, G_5, T_7, G_7, F_7) → veelhoek29, b_{12}, c_{12}, d_{12}, e_{12}, f_{13}
  229. Mirror(veelhoek24, x = 4) → veelhoek24'
  230. Mirror(E_7, x = 4) → U_7
  231. Mirror(F_7, x = 4) → V_7
  232. Polygon(F_5, E_5, F_6, U_7, V_7) → veelhoek30, g_{13}, h_{13}, i_{13}, u_7, v_7
  233. Mirror(G_7, x = 4) → W_7
  234. Polygon(G_5, F_5, V_7, W_7, T_7) → veelhoek31, j_{13}, k_{13}, l_{13}, w_7, m_{13}
  235. Mirror(D_7, x = 4) → Z_7
  236. Mirror(T_4, x = 4) → A_8
  237. Mirror(A_5, x = 4) → B_8
  238. Polygon(Z_7, U_7, F_6, B_8, A_8) → veelhoek32, z_7, n_{13}, p_{13}, q_{13}, r_{13}
  239. Polygon(Z_6, A_8, B_8, K_6, L_6) → veelhoek33, z_6, s_{13}, t_{13}, a_{13}, b_{13}
  240. Mirror(P_7, x = 4) → C_8
  241. Polygon(C_8, Z_7, A_8, Z_6, W_6) → veelhoek34, c_{13}, d_{13}, e_{13}, f_{14}, w_6
  242. Mirror(veelhoek7, xAxis) → veelhoek7'
  243. Mirror(R_7, x = 4) → D_8
  244. Mirror(O_7, x = 4) → E_8
  245. Polygon(E_8, C_8, W_6, V_6, D_8) → veelhoek35, g_{14}, h_{14}, i_{14}, v_6, j_{14}
  246. Intersect(e_2, xAxis) → F_8
  247. Intersect(m_2, xAxis) → G_8
  248. Midpoint(S_3, Q_7) → H_8
  249. Polygon(H_8, Q_7, R_7, F_8) → vierhoek4, k_{14}, l_{14}, m_{14}, n_{14}
  250. Mirror(R_7, xAxis) → I_8
  251. Polygon(I_8, F_8, R_7, O_7, N_7) → veelhoek36, p_{14}, q_{14}, r_{14}, s_{14}, t_{14}
  252. Mirror(I_8, x = 4) → J_8
  253. Mirror(H_8, x = 4) → K_8
  254. Polygon(V_6, K_8, G_8, D_8) → vierhoek5, a_{14}, b_{14}, c_{14}, d_{14}
  255. Mirror(N_7, x = 4) → L_8
  256. Polygon(L_8, E_8, D_8, G_8, J_8) → veelhoek37, e_{14}, f_{15}, g_{15}, h_{15}, i_{15}
  257. Mirror(Q_7, xAxis) → M_8
  258. Mirror(Q_3, xAxis) → N_8
  259. Mirror(P_7, xAxis) → O_8
  260. Mirror(O_7, xAxis) → P_8
  261. Mirror(R_7, xAxis) → Q_8
  262. Polygon(M_8, N_8, O_8, P_8, Q_8) → veelhoek27', j_{15}, k_{15}, o_8, l_{15}, m_{15}
  263. Mirror(H_8, xAxis) → R_8
  264. Mirror(Q_7, xAxis) → S_8
  265. Mirror(R_7, xAxis) → T_8
  266. Mirror(F_8, xAxis) → U_8
  267. Polygon(R_8, S_8, T_8, U_8) → vierhoek4', n_{15}, p_{15}, q_{15}, u_8
  268. Mirror(N_8, x = 4) → V_8
  269. Mirror(M_8, x = 4) → W_8
  270. Mirror(M_7, x = 4) → Z_8
  271. Polygon(L_8, J_8, W_8, V_8, Z_8) → veelhoek38, r_{15}, s_{15}, w_8, v_8, z_8
  272. Mirror(veelhoek22, xAxis) → veelhoek22'
  273. Mirror(R_8, x = 4) → A_9
  274. Polygon(A_9, W_8, J_8, G_8) → vierhoek6, t_{15}, a_{15}, b_{15}, c_{15}
  275. Mirror(P_3, xAxis) → B_9
  276. Mirror(O_3, xAxis) → C_9
  277. Mirror(K_3, xAxis) → E_9
  278. Mirror(L_3, xAxis) → D_9
  279. Mirror(T_4, xAxis) → F_9
  280. Polygon(F_9, B_9, N_8, M_7, L_7) → veelhoek39, d_{15}, e_{15}, f_{16}, g_{16}, h_{16}
  281. Mirror(A_5, xAxis) → G_9
  282. Mirror(J_5, xAxis) → H_9
  283. Polygon(G_9, F_9, L_7, K_7, H_9) → veelhoek40, i_{16}, j_{16}, k_{16}, l_{16}, m_{16}
  284. Mirror(I_5, xAxis) → I_9
  285. Mirror(H_5, xAxis) → J_9
  286. Polygon(J_9, I_9, H_9, K_7, J_7) → veelhoek41, n_{16}, p_{16}, q_{16}, r_{16}, s_{16}
  287. Mirror(G_5, xAxis) → K_9
  288. Mirror(T_7, xAxis) → L_9
  289. Polygon(J_7, I_7, L_9, K_9, J_9) → veelhoek42, t_{16}, a_{16}, b_{16}, c_{16}, d_{16}
  290. Mirror(I_7, x = 4) → M_9
  291. Mirror(H_7, x = 4) → N_9
  292. Polygon(N_9, H_7, G_7, T_7, W_7) → veelhoek43, e_{16}, f_{17}, g_{17}, h_{17}, i_{17}
  293. Polygon(L_9, I_7, H_7, N_9, M_9) → veelhoek44, j_{17}, k_{17}, l_{17}, m_{17}, n_{17}
  294. Mirror(G_5, xAxis) → O_9
  295. Mirror(F_5, xAxis) → P_9
  296. Mirror(V_7, xAxis) → Q_9
  297. Mirror(W_7, xAxis) → R_9
  298. Mirror(T_7, xAxis) → S_9
  299. Polygon(O_9, P_9, Q_9, R_9, S_9) → veelhoek31', o_9, p_{17}, q_{17}, r_{17}, s_{17}
  300. Mirror(F_5, xAxis) → T_9
  301. Mirror(E_5, xAxis) → U_9
  302. Mirror(F_6, xAxis) → V_9
  303. Mirror(U_7, xAxis) → W_9
  304. Mirror(V_7, xAxis) → Z_9
  305. Polygon(T_9, U_9, V_9, W_9, Z_9) → veelhoek30', t_{17}, u_9, v_9, w_9, z_9
  306. Mirror(Z_7, xAxis) → A_{10}
  307. Mirror(U_7, xAxis) → B_{10}
  308. Mirror(F_6, xAxis) → C_{10}
  309. Mirror(B_8, xAxis) → D_{10}
  310. Mirror(A_8, xAxis) → E_{10}
  311. Polygon(A_{10}, B_{10}, C_{10}, D_{10}, E_{10}) → veelhoek32', a_{17}, b_{17}, c_{17}, d_{17}, e_{17}
  312. Mirror(C_8, xAxis) → F_{10}
  313. Mirror(Z_7, xAxis) → G_{10}
  314. Mirror(A_8, xAxis) → H_{10}
  315. Mirror(Z_6, xAxis) → I_{10}
  316. Mirror(W_6, xAxis) → J_{10}
  317. Polygon(F_{10}, G_{10}, H_{10}, I_{10}, J_{10}) → veelhoek34', f_{18}, g_{18}, h_{18}, i_{18}, j_{18}
  318. Mirror(M_4, xAxis) → K_{10}
  319. Polygon(B_9, F_9, G_9, K_{10}, C_9) → veelhoek45, k_{18}, l_{18}, m_{18}, n_{18}, p_{18}
  320. Mirror(C_9, x = 4) → L_{10}
  321. Polygon(I_3, U_2, I_{10}, L_{10}, R_2) → veelhoek46, q_{18}, u_2, r_{18}, s_{18}, t_{18}
  322. Mirror(N_3, xAxis) → M_{10}
  323. Mirror(N_4, xAxis) → N_{10}
  324. Polygon(E_9, C_9, K_{10}, N_{10}, M_{10}) → veelhoek47, a_{18}, b_{18}, c_{18}, d_{18}, e_{18}
  325. Mirror(H_3, xAxis) → O_{10}
  326. Mirror(M_3, xAxis) → P_{10}
  327. Polygon(D_9, E_9, M_{10}, P_{10}, O_{10}) → veelhoek48, f_{19}, g_{19}, h_{19}, i_{19}, o_{10}
  328. Mirror(veelhoek15, xAxis) → veelhoek15'
  329. Mirror(V_4, xAxis) → Q_{10}
  330. Mirror(W_4, xAxis) → R_{10}
  331. Polygon(R_{10}, Q_{10}, G_9, H_9, I_9) → veelhoek49, j_{19}, k_{19}, l_{19}, m_{19}, n_{19}
  332. Mirror(I_4, xAxis) → S_{10}
  333. Polygon(S_{10}, N_{10}, K_{10}, G_9, Q_{10}) → veelhoek50, p_{19}, q_{19}, r_{19}, s_{19}, t_{19}
  334. Mirror(R_{10}, x = 4) → T_{10}
  335. Mirror(Q_{10}, x = 4) → U_{10}
  336. Polygon(T_{10}, U_9, T_2, I_3, U_{10}) → veelhoek51, a_{19}, b_{19}, c_{19}, d_{19}, u_{10}
  337. Mirror(L_1, x = 4) → V_{10}
  338. Mirror(S_{10}, x = 4) → W_{10}
  339. Mirror(N_{10}, x = 4) → Z_{10}
  340. Polygon(Z_{10}, W_{10}, U_{10}, I_3, R_2) → veelhoek52, z_{10}, w_{10}, e_{19}, f_{20}, g_{20}
  341. Mirror(M_{10}, x = 4) → A_{11}
  342. Mirror(E_9, x = 4) → B_{11}
  343. Polygon(A_{11}, Z_{10}, R_2, L_{10}, B_{11}) → veelhoek53, h_{20}, i_{20}, j_{20}, k_{20}, l_{20}
  344. Mirror(P_{10}, x = 4) → C_{11}
  345. Mirror(O_{10}, x = 4) → D_{11}
  346. Mirror(D_9, x = 4) → E_{11}
  347. Polygon(E_{11}, D_{11}, C_{11}, A_{11}, B_{11}) → veelhoek54, m_{20}, n_{20}, p_{20}, q_{20}, r_{20}
  348. Mirror(veelhoek8, xAxis) → veelhoek8'_1
  349. Mirror(veelhoek8', xAxis) → veelhoek8''
  350. Mirror(C_7, xAxis) → F_{11}
  351. Polygon(F_2, F_{11}, C_{11}, D_{11}) → vierhoek7, s_{20}, t_{20}, a_{20}, b_{20}
  352. Mirror(F_{11}, x = 4) → G_{11}
  353. Polygon(E_2, O_{10}, P_{10}, G_{11}) → vierhoek8, c_{20}, d_{20}, e_{20}, f_{21}
  354. Mirror(G_4, xAxis) → H_{11}
  355. Mirror(H_4, xAxis) → I_{11}
  356. Mirror(R_4, xAxis) → J_{11}
  357. Polygon(I_{11}, S_{10}, Q_{10}, R_{10}, J_{11}) → veelhoek55, g_{21}, h_{21}, i_{21}, j_{21}, k_{21}
  358. Mirror(U_4, xAxis) → K_{11}
  359. Mirror(O_4, xAxis) → L_{11}
  360. Polygon(H_{11}, I_{11}, J_{11}, K_{11}, L_{11}) → veelhoek56, l_{21}, m_{21}, n_{21}, p_{21}, q_{21}
  361. Mirror(F_4, xAxis) → M_{11}
  362. Mirror(Q_4, xAxis) → N_{11}
  363. Polygon(M_{11}, H_{11}, L_{11}, M_2, N_{11}) → veelhoek57, r_{21}, s_{21}, t_{21}, a_{21}, b_{21}
  364. Mirror(B_5, xAxis) → O_{11}
  365. Polygon(K_{11}, O_{11}, L_2, M_2, L_{11}) → veelhoek58, c_{21}, o_{11}, d_{21}, e_{21}, f_{22}
  366. Mirror(C_5, xAxis) → P_{11}
  367. Mirror(T_5, xAxis) → Q_{11}
  368. Polygon(P_{11}, Q_{11}, W_{10}, U_{10}, T_{10}) → veelhoek59, g_{22}, h_{22}, i_{22}, j_{22}, k_{22}
  369. Mirror(K_5, xAxis) → R_{11}
  370. Polygon(O_{11}, P_{11}, Q_{11}, R_{11}, L_2) → veelhoek60, l_{22}, m_{22}, n_{22}, p_{22}, q_{22}
  371. Mirror(L_5, xAxis) → S_{11}
  372. Mirror(M_5, xAxis) → T_{11}
  373. Polygon(A'_2, M_2, L_2, R_{11}, S_{11}) → veelhoek61, a'_2, r_{22}, s_{22}, t_{22}, a_{22}
  374. Polygon(T_{11}, M_2, L_2, R_{11}, S_{11}) → veelhoek62, b_{22}, c_{22}, d_{22}, e_{22}, f_{23}
  375. Segment(Z_1, MM) → g_{23}
  376. Segment(MM, A_2) → h_{23}
  377. Segment(U_1, V_1) → i_{23}
  378. Segment(V_1, B_2) → j_{23}
  379. Segment(C_2, O) → k_{23}
  380. Segment(D_2, K) → l_{23}
  381. Segment(O, A_3) → m_{23}
  382. Segment(K, RO) → n_{23}
  383. Segment(O, K) → p_{23}
  384. Segment(MM, M_2) → q_{23}
  385. Segment(V_1, N_5) → r_{23}

AI Drawing Prompt Reference

Draw an Islamic geometric pattern with a 13-sided polygon. Start by creating point A on the x-axis and rotate it 13 times with an angle of 360 degrees/13 to form the first 13-sided polygon. Then create point K on the x-axis and rotate it 13 times to form the second 13-sided polygon. Use the perpendicular bisector to find the symmetry axis, and construct multiple smaller polygons using distance, rotation, and other commands. Finally, apply mirroring, translation, and rotation to create a complex symmetric pattern.
The prompt above was compiled from the original drawing commands and is for reference only.