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Islamic Geometric Line Patterns

Islamic Geometric Line Patterns
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2019-12-31 17:18
PolygonTransformationGeometric Construction
This example demonstrates the symmetric arrangement and transformations of lines in Islamic geometric patterns. Key math concepts include symmetry, geometric transformations, polygon construction, vector operations, etc. Construction highlights GeoGebra commands like Rotate, Polygon, Midpoint, Vector, Translate, OrthogonalLine, Mirror, Segment, Line, PolyLine, Centroid, Intersect, Angle, Ray, Point, FractionText, and Circle. Suitable for high school and above students learning geometric constructions and transformations, or for art and design education.

GeoGebra Commands & Parameters

  1. ConstructionStep() → stap
  2. Rotate(A, ((-(360°))) / 7) → B
  3. Polygon(B, A, 7) → veelhoek1, f, E, F, G, g, h, i, j, k, l, C, D
  4. Rotate(O, hoekb, H) → J
  5. Rotate(H, hoekb, J) → K
  6. Rotate(J, hoeka, K) → L
  7. Polygon(O, I, L, K, J, H) → veelhoek2, o, i_1, l_1, k_1, j_1, h_1
  8. Rotate(H, hoeka) → M
  9. Rotate(O, hoekd, I) → N
  10. Rotate(O, (-hoekd), M) → P
  11. Rotate(I, hoekd, N) → Q
  12. Polygon(I, N, Q, P, M, O) → veelhoek3, i_2, n, q, p, m, o_1
  13. Midpoint(q) → R
  14. Midpoint(n) → S
  15. Midpoint(i_2) → T
  16. Midpoint(p) → U
  17. Vector(P, J) → u
  18. Translate(I, u) → I'
  19. Translate(N, u) → N'
  20. Translate(Q, u) → Q'
  21. Translate(P, u) → P'
  22. Translate(M, u) → M'
  23. Translate(O, u) → O'
  24. Polygon(I', N', Q', P', M', O') → veelhoek3', i', n', q', p', m', o'
  25. Translate(O, Vector[(-u)]) → O'_1
  26. Translate(I, Vector[(-u)]) → I'_1
  27. Translate(L, Vector[(-u)]) → L'
  28. Translate(K, Vector[(-u)]) → K'
  29. Translate(J, Vector[(-u)]) → J'
  30. Translate(H, Vector[(-u)]) → H'
  31. Polygon(O'_1, I'_1, L', K', J', H') → veelhoek2', o'_1, i'_1, l', k', j', h'
  32. Rotate(I, hoeka, L) → V
  33. Rotate(L, hoekb, V) → W
  34. Rotate(V, hoekb, W) → V'
  35. Polygon(L, I, N, V', W, V) → veelhoek4, l_2, i_3, n_1, v', w, v
  36. Translate(L, Vector[(-u)]) → L'_1
  37. Translate(I, Vector[(-u)]) → I'_2
  38. Translate(N, Vector[(-u)]) → N'_1
  39. Translate(V', Vector[(-u)]) → V''
  40. Translate(W, Vector[(-u)]) → W'
  41. Translate(V, Vector[(-u)]) → V'_1
  42. Polygon(L'_1, I'_2, N'_1, V'', W', V'_1) → veelhoek4', l'_1, i'_2, n'_1, v'', w', v'_1
  43. Rotate(N, hoekb, V') → N'_2
  44. Polygon(Q, L', V'_1, N'_2, V', N) → veelhoek5, q_1, r, s, n'_2, t, n_2
  45. Translate(Q, Vector[(-u)]) → Q'_1
  46. Translate(L', Vector[(-u)]) → L''
  47. Translate(V'_1, Vector[(-u)]) → Z
  48. Translate(N'_2, Vector[(-u)]) → A_1
  49. Translate(V', Vector[(-u)]) → V''_1
  50. Translate(N, Vector[(-u)]) → N'_3
  51. Polygon(Q'_1, L'', Z, A_1, V''_1, N'_3) → veelhoek5', q'_1, l'', z_1, a_1, v''_1, n'_3
  52. Translate(Q, u) → Q'_2
  53. Translate(L', u) → L''_1
  54. Translate(V'_1, u) → B_1
  55. Translate(N'_2, u) → C_1
  56. Translate(V', u) → V''_2
  57. Translate(N, u) → N'_4
  58. Polygon(Q'_2, L''_1, B_1, C_1, V''_2, N'_4) → veelhoek5'_1, q'_2, l''_1, b_1, c_1, v''_2, n'_4
  59. Translate(I, Vector[(-u)]) → I'_3
  60. Translate(N, Vector[(-u)]) → N'_5
  61. Translate(Q, Vector[(-u)]) → Q'_3
  62. Translate(P, Vector[(-u)]) → P'_1
  63. Translate(M, Vector[(-u)]) → M'_1
  64. Translate(O, Vector[(-u)]) → O'_2
  65. Polygon(I'_3, N'_5, Q'_3, P'_1, M'_1, O'_2) → veelhoek3'_1, i'_3, n'_5, q'_3, p'_1, m'_1, o'_2
  66. Translate(Q, uu) → Q'_4
  67. Translate(L', uu) → L''_2
  68. Translate(V'_1, uu) → D_1
  69. Translate(N'_2, uu) → E_1
  70. Translate(V', uu) → V''_3
  71. Translate(N, uu) → N'_6
  72. Polygon(Q'_4, L''_2, D_1, E_1, V''_3, N'_6) → veelhoek5'_2, q'_4, l''_2, d_1, e_1, v''_3, n'_6
  73. Translate(L'_1, uu) → F_1
  74. Translate(I'_2, uu) → G_1
  75. Translate(N'_1, uu) → H_1
  76. Translate(V'', uu) → V'''
  77. Translate(W', uu) → W''
  78. Translate(V'_1, uu) → I_1
  79. Polygon(F_1, G_1, H_1, V''', W'', I_1) → veelhoek4'', f_1, g_1, a, v''', w'', b
  80. Translate(L, uu) → L'_2
  81. Translate(I, uu) → I'_4
  82. Translate(N, uu) → N'_7
  83. Translate(V', uu) → V''_4
  84. Translate(W, uu) → W'_1
  85. Translate(V, uu) → V'_2
  86. Polygon(L'_2, I'_4, N'_7, V''_4, W'_1, V'_2) → veelhoek4'_1, l'_2, i'_4, n'_7, v''_4, w'_1, v'_2
  87. Translate(I, uu) → I'_5
  88. Translate(N, uu) → N'_8
  89. Translate(Q, uu) → Q'_5
  90. Translate(P, uu) → P'_2
  91. Translate(M, uu) → M'_2
  92. Translate(O, uu) → O'_3
  93. Polygon(I'_5, N'_8, Q'_5, P'_2, M'_2, O'_3) → veelhoek3'_2, i'_5, n'_8, q'_5, p'_2, m'_2, o'_3
  94. Translate(L, u) → L'_3
  95. Translate(I, u) → I'_6
  96. Translate(N, u) → N'_9
  97. Translate(V', u) → V''_5
  98. Translate(W, u) → W'_2
  99. Translate(V, u) → V'_3
  100. Polygon(L'_3, I'_6, N'_9, V''_5, W'_2, V'_3) → veelhoek4'_2, l'_3, i'_6, n'_9, v''_5, w'_2, v'_3
  101. Translate(I, Vector[(-uu)]) → I'_7
  102. Translate(N, Vector[(-uu)]) → N'_{10}
  103. Translate(Q, Vector[(-uu)]) → Q'_6
  104. Translate(P, Vector[(-uu)]) → P'_3
  105. Translate(M, Vector[(-uu)]) → M'_3
  106. Translate(O, Vector[(-uu)]) → O'_4
  107. Polygon(I'_7, N'_{10}, Q'_6, P'_3, M'_3, O'_4) → veelhoek3'_3, i'_7, n'_{10}, q'_6, p'_3, m'_3, o'_4
  108. Translate(Q, Vector[(-uu)]) → Q'_7
  109. Translate(L', Vector[(-uu)]) → L''_3
  110. Translate(V'_1, Vector[(-uu)]) → J_1
  111. Translate(N'_2, Vector[(-uu)]) → K_1
  112. Translate(V', Vector[(-uu)]) → V''_6
  113. Translate(N, Vector[(-uu)]) → N'_{11}
  114. Polygon(Q'_7, L''_3, J_1, K_1, V''_6, N'_{11}) → veelhoek5'_3, q'_7, l''_3, c, d, v''_6, n'_{11}
  115. Translate(O'_1, Vector[(-uu)]) → L_1
  116. Translate(I'_1, Vector[(-uu)]) → M_1
  117. Translate(L', Vector[(-uu)]) → L''_4
  118. Translate(K', Vector[(-uu)]) → K''
  119. Translate(J', Vector[(-uu)]) → J''
  120. Translate(H', Vector[(-uu)]) → H''
  121. Polygon(L_1, M_1, L''_4, K'', J'', H'') → veelhoek2'', e, m_1, l''_4, k'', j'', h''
  122. Translate(O, Vector[(-uu)]) → O'_5
  123. Translate(I, Vector[(-uu)]) → I'_8
  124. Translate(L, Vector[(-uu)]) → L'_4
  125. Translate(K, Vector[(-uu)]) → K'_1
  126. Translate(J, Vector[(-uu)]) → J'_1
  127. Translate(H, Vector[(-uu)]) → H'_1
  128. Polygon(O'_5, I'_8, L'_4, K'_1, J'_1, H'_1) → veelhoek2'_1, o'_5, i'_8, l'_4, k'_1, j'_1, h'_1
  129. Translate(L, Vector[(-uu)]) → L'_5
  130. Translate(I, Vector[(-uu)]) → I'_9
  131. Translate(N, Vector[(-uu)]) → N'_{12}
  132. Translate(V', Vector[(-uu)]) → V''_7
  133. Translate(W, Vector[(-uu)]) → W'_3
  134. Translate(V, Vector[(-uu)]) → V'_4
  135. Polygon(L'_5, I'_9, N'_{12}, V''_7, W'_3, V'_4) → veelhoek4'_3, l'_5, i'_9, n'_{12}, v''_7, w'_3, v'_4
  136. Translate(I', Vector[(-uu)]) → I''
  137. Translate(N', Vector[(-uu)]) → N''
  138. Translate(Q', Vector[(-uu)]) → Q''
  139. Translate(P', Vector[(-uu)]) → P''
  140. Translate(M', Vector[(-uu)]) → M''
  141. Translate(O', Vector[(-uu)]) → O''
  142. Polygon(I'', N'', Q'', P'', M'', O'') → veelhoek3'', i'', n'', q'', p'', m'', o''
  143. Translate(O'_5, u) → N_1
  144. Translate(I'_8, u) → O_1
  145. Translate(L'_4, u) → P_1
  146. Translate(K'_1, u) → Q_1
  147. Translate(J'_1, u) → R_1
  148. Translate(H'_1, u) → S_1
  149. Polygon(N_1, O_1, P_1, Q_1, R_1, S_1) → veelhoek6, p_1, r_1, s_1, t_1, f_2, g_2
  150. Translate(Q'_7, u) → T_1
  151. Translate(L''_3, u) → U_1
  152. Translate(J_1, u) → V_1
  153. Translate(K_1, u) → W_1
  154. Translate(V''_6, u) → Z_1
  155. Translate(N'_{11}, u) → A_2
  156. Polygon(T_1, U_1, V_1, W_1, Z_1, A_2) → veelhoek7, h_2, u_1, v_1, w_1, j_2, a_2
  157. Translate(I'_3, Vector[(-uu)]) → B_2
  158. Translate(N'_5, Vector[(-uu)]) → C_2
  159. Translate(Q'_3, Vector[(-uu)]) → D_2
  160. Translate(P'_1, Vector[(-uu)]) → E_2
  161. Translate(M'_1, Vector[(-uu)]) → F_2
  162. Translate(O'_2, Vector[(-uu)]) → G_2
  163. Polygon(B_2, C_2, D_2, E_2, F_2, G_2) → veelhoek8, b_2, c_2, d_2, e_2, k_2, m_2
  164. Translate(L'_1, Vector[(-u)]) → H_2
  165. Translate(I'_2, Vector[(-u)]) → I_2
  166. Translate(N'_1, Vector[(-u)]) → J_2
  167. Translate(V'', Vector[(-u)]) → V'''_1
  168. Translate(W', Vector[(-u)]) → W''_1
  169. Translate(V'_1, Vector[(-u)]) → K_2
  170. Polygon(H_2, I_2, J_2, V'''_1, W''_1, K_2) → veelhoek4''_1, p_2, q_2, r_2, v'''_1, w''_1, s_2
  171. Translate(L'_1, Vector[(-uu)]) → L_2
  172. Translate(I'_2, Vector[(-uu)]) → M_2
  173. Translate(N'_1, Vector[(-uu)]) → N_2
  174. Translate(V'', Vector[(-uu)]) → V'''_2
  175. Translate(W', Vector[(-uu)]) → W''_2
  176. Translate(V'_1, Vector[(-uu)]) → O_2
  177. Polygon(L_2, M_2, N_2, V'''_2, W''_2, O_2) → veelhoek4''_2, t_2, f_3, g_3, v'''_2, w''_2, o_2
  178. Translate(I'_7, Vector[(-uu)]) → P_2
  179. Translate(N'_{10}, Vector[(-uu)]) → Q_2
  180. Translate(Q'_6, Vector[(-uu)]) → R_2
  181. Translate(P'_3, Vector[(-uu)]) → S_2
  182. Translate(M'_3, Vector[(-uu)]) → T_2
  183. Translate(O'_4, Vector[(-uu)]) → U_2
  184. Polygon(P_2, Q_2, R_2, S_2, T_2, U_2) → veelhoek9, h_3, j_3, k_3, l_3, m_3, u_2
  185. Translate(O'_5, Vector[(-uu)]) → V_2
  186. Translate(I'_8, Vector[(-uu)]) → W_2
  187. Translate(L'_4, Vector[(-uu)]) → Z_2
  188. Translate(K'_1, Vector[(-uu)]) → A_3
  189. Translate(J'_1, Vector[(-uu)]) → B_3
  190. Translate(H'_1, Vector[(-uu)]) → C_3
  191. Polygon(V_2, W_2, Z_2, A_3, B_3, C_3) → veelhoek10, v_2, w_2, z_2, a_3, b_3, c_3
  192. OrthogonalLine(G, o) → n_3
  193. Mirror(F, n_3) → F'
  194. Mirror(G, n_3) → G'
  195. Segment(F', G') → k'_2
  196. OrthogonalLine(D, m) → p_3
  197. Mirror(D, p_3) → D'
  198. Mirror(E, p_3) → E'
  199. Segment(D', E') → i'_{10}
  200. Midpoint(i_2) → D_3
  201. Midpoint(p) → E_3
  202. Line(D_3, E_3) → q_3
  203. Mirror(F', q_3) → F''
  204. Mirror(G', q_3) → G''
  205. Segment(F'', G'') → r_3
  206. Mirror(F, q_3) → F'_1
  207. Mirror(G, q_3) → G'_1
  208. Segment(F'_1, G'_1) → k'_3
  209. Mirror(E, q_3) → E'_1
  210. Mirror(F, q_3) → F'_2
  211. Segment(E'_1, F'_2) → j'_2
  212. Mirror(D, q_3) → D'_1
  213. Mirror(E, q_3) → E'_2
  214. Segment(D'_1, E'_2) → i'_{11}
  215. Mirror(E', q_3) → E''
  216. PolyLine(D_3, F', E'_1, F'_1, G'', F'', D_3, G, F, E, D, E', E_3, E'', D'_1) → recht
  217. Centroid(veelhoek2) → F_3
  218. Mirror(B, F_3) → B'
  219. Midpoint(k_1) → G_3
  220. Midpoint(l_1) → H_3
  221. Intersect(o, h_1) → I_3
  222. Angle(C, A, I_3) → snij
  223. Midpoint(i_1) → J_3
  224. Midpoint(j_1) → K_3
  225. Intersect(k_1, j_1) → L_3
  226. Rotate(L_3, (-snij), K_3) → M_3
  227. Ray(K_3, M_3) → e_3
  228. Rotate(L_3, snij, G_3) → N_3
  229. Ray(G_3, N_3) → f_4
  230. Intersect(e_3, f_4) → O_3
  231. Mirror(O_3, Line[K_3, J_3]) → P_3
  232. Intersect(l_1, k_1) → Q_3
  233. Mirror(O_3, Line[Q_3, I_3]) → R_3
  234. Mirror(P_3, Line[Q_3, I_3]) → S_3
  235. PolyLine(H_3, B', J_3, R_3, H_3, G_3, O_3, K_3, P_3, A, B, G, S_3) → kringLB
  236. Centroid(veelhoek4) → T_3
  237. Mirror(H_3, h_1) → U_3
  238. Mirror(B', h_1) → B''
  239. Mirror(G_3, h_1) → V_3
  240. Mirror(O_3, h_1) → W_3
  241. Mirror(K_3, h_1) → Z_3
  242. Mirror(P_3, h_1) → A_4
  243. Mirror(A, h_1) → A'
  244. Mirror(B, h_1) → B'_1
  245. Mirror(G, h_1) → G'_2
  246. Mirror(S_3, h_1) → B_4
  247. Mirror(J_3, h_1) → C_4
  248. Mirror(R_3, h_1) → D_4
  249. Mirror(H_3, h_1) → E_4
  250. PolyLine(U_3, B'', C_4, D_4, E_4, V_3, W_3, Z_3, A_4, A', B'_1, G'_2, B_4) → kringLO
  251. Mirror(H_3, q_3) → F_4
  252. Mirror(B', q_3) → B''_1
  253. Mirror(G_3, q_3) → G_4
  254. Mirror(O_3, q_3) → H_4
  255. Mirror(K_3, q_3) → I_4
  256. Mirror(P_3, q_3) → J_4
  257. Mirror(A, q_3) → A'_1
  258. Mirror(B, q_3) → B'_2
  259. Mirror(G, q_3) → G'_3
  260. Mirror(S_3, q_3) → K_4
  261. Mirror(J_3, q_3) → L_4
  262. Mirror(R_3, q_3) → M_4
  263. Mirror(H_3, q_3) → N_4
  264. PolyLine(F_4, B''_1, L_4, M_4, N_4, G_4, H_4, I_4, J_4, A'_1, B'_2, G'_3, K_4) → kringRB
  265. Mirror(U_3, q_3) → O_4
  266. Mirror(B'', q_3) → B'''
  267. Mirror(V_3, q_3) → P_4
  268. Mirror(W_3, q_3) → Q_4
  269. Mirror(Z_3, q_3) → R_4
  270. Mirror(A_4, q_3) → S_4
  271. Mirror(A', q_3) → A''
  272. Mirror(B'_1, q_3) → T_4
  273. Mirror(G'_2, q_3) → U_4
  274. Mirror(B_4, q_3) → V_4
  275. Mirror(C_4, q_3) → W_4
  276. Mirror(D_4, q_3) → Z_4
  277. Mirror(E_4, q_3) → A_5
  278. PolyLine(O_4, B''', W_4, Z_4, A_5, P_4, Q_4, R_4, S_4, A'', T_4, U_4, V_4) → kringRO
  279. Ray(E'', E_3) → s_3
  280. Ray(D_4, C_4) → t_3
  281. Ray(E', E_3) → d_3
  282. Ray(Z_4, W_4) → g_4
  283. Intersect(s_3, t_3) → B_5
  284. Intersect(d_3, g_4) → C_5
  285. Ray(B_4, C_4) → h_4
  286. Ray(V_4, W_4) → i_4
  287. Intersect(q_3, g_1) → D_5
  288. Centroid(veelhoek4'') → E_5
  289. Mirror(B_5, E_5) → F_5
  290. Mirror(C_5, E_5) → G_5
  291. Midpoint(f_1) → H_5
  292. Midpoint(a) → I_5
  293. Segment(H_5, G_5) → j_4
  294. Segment(G_5, D_5) → k_4
  295. Segment(D_5, F_5) → l_4
  296. Segment(F_5, I_5) → m_4
  297. Segment(E_3, B_5) → n_4
  298. Segment(B_5, C_4) → p_4
  299. Segment(E_3, C_5) → q_4
  300. Segment(W_4, C_5) → r_4
  301. Ray(B_4, C_4) → s_4
  302. Ray(V_4, W_4) → t_4
  303. Intersect(q'_4, l''_2) → K_5
  304. Intersect(j', a) → L_5
  305. Segment(K_5, L_5) → a_4
  306. Intersect(s_4, a_4) → M_5
  307. Intersect(t_4, a_4) → N_5
  308. PolyLine(E_3, B_5, W_4, C_5, E_3, C_4, M_5, H_5, G_5, D_5, F_5, I_5, N_5) → kringhor
  309. Translate(E_3, Vector[E_5, T_3]) → O_5
  310. Translate(B_5, Vector[E_5, T_3]) → P_5
  311. Translate(C_4, Vector[E_5, T_3]) → Q_5
  312. Translate(M_5, Vector[E_5, T_3]) → R_5
  313. Translate(H_5, Vector[E_5, T_3]) → S_5
  314. Translate(G_5, Vector[E_5, T_3]) → T_5
  315. Translate(D_5, Vector[E_5, T_3]) → U_5
  316. Translate(F_5, Vector[E_5, T_3]) → V_5
  317. Translate(I_5, Vector[E_5, T_3]) → W_5
  318. Translate(N_5, Vector[E_5, T_3]) → Z_5
  319. Translate(W_4, Vector[E_5, T_3]) → A_6
  320. Translate(C_5, Vector[E_5, T_3]) → B_6
  321. Translate(E_3, Vector[E_5, T_3]) → C_6
  322. PolyLine(O_5, P_5, A_6, B_6, C_6, Q_5, R_5, S_5, T_5, U_5, V_5, W_5, Z_5) → kringhor'
  323. Translate(D_3, Vector[(-uu)]) → D_6
  324. Translate(F', Vector[(-uu)]) → F''_1
  325. Translate(G, Vector[(-uu)]) → G'_4
  326. Translate(F, Vector[(-uu)]) → F'_3
  327. Translate(E, Vector[(-uu)]) → E'_3
  328. Translate(D, Vector[(-uu)]) → D'_2
  329. Translate(E', Vector[(-uu)]) → E''_1
  330. Translate(E_3, Vector[(-uu)]) → E_6
  331. Translate(E'', Vector[(-uu)]) → E'''
  332. Translate(D'_1, Vector[(-uu)]) → F_6
  333. Translate(E'_1, Vector[(-uu)]) → G_6
  334. Translate(F'_1, Vector[(-uu)]) → H_6
  335. Translate(G'', Vector[(-uu)]) → G'''
  336. Translate(F'', Vector[(-uu)]) → F'''
  337. Translate(D_3, Vector[(-uu)]) → I_6
  338. PolyLine(D_6, F''_1, G_6, H_6, G''', F''', I_6, G'_4, F'_3, E'_3, D'_2, E''_1, E_6, E''', F_6) → recht'
  339. Translate(D_3, u) → J_6
  340. Translate(F', u) → F''_2
  341. Translate(G, u) → G'_5
  342. Translate(F, u) → F'_4
  343. Translate(E, u) → E'_4
  344. Translate(D, u) → D'_3
  345. Translate(E', u) → E''_2
  346. Translate(E_3, u) → K_6
  347. Translate(E'', u) → E'''_1
  348. Translate(D'_1, u) → L_6
  349. Translate(E'_1, u) → M_6
  350. Translate(F'_1, u) → N_6
  351. Translate(G'', u) → G'''_1
  352. Translate(F'', u) → F'''_1
  353. Translate(D_3, u) → O_6
  354. PolyLine(J_6, F''_2, M_6, N_6, G'''_1, F'''_1, O_6, G'_5, F'_4, E'_4, D'_3, E''_2, K_6, E'''_1, L_6) → recht'_1
  355. Translate(D_6, u) → P_6
  356. Translate(F''_1, u) → Q_6
  357. Translate(G'_4, u) → R_6
  358. Translate(F'_3, u) → S_6
  359. Translate(E'_3, u) → T_6
  360. Translate(D'_2, u) → U_6
  361. Translate(E''_1, u) → V_6
  362. Translate(E_6, u) → W_6
  363. Translate(E''', u) → Z_6
  364. Translate(F_6, u) → A_7
  365. Translate(G_6, u) → B_7
  366. Translate(H_6, u) → C_7
  367. Translate(G''', u) → D_7
  368. Translate(F''', u) → E_7
  369. Translate(I_6, u) → F_7
  370. PolyLine(P_6, Q_6, B_7, C_7, D_7, E_7, F_7, R_6, S_6, T_6, U_6, V_6, W_6, Z_6, A_7) → recht''
  371. Translate(D_6, Vector[(-u)]) → G_7
  372. Translate(F''_1, Vector[(-u)]) → H_7
  373. Translate(G'_4, Vector[(-u)]) → I_7
  374. Translate(F'_3, Vector[(-u)]) → J_7
  375. Translate(E'_3, Vector[(-u)]) → K_7
  376. Translate(D'_2, Vector[(-u)]) → L_7
  377. Translate(E''_1, Vector[(-u)]) → M_7
  378. Translate(E_6, Vector[(-u)]) → N_7
  379. Translate(E''', Vector[(-u)]) → O_7
  380. Translate(F_6, Vector[(-u)]) → P_7
  381. Translate(G_6, Vector[(-u)]) → Q_7
  382. Translate(H_6, Vector[(-u)]) → R_7
  383. Translate(G''', Vector[(-u)]) → S_7
  384. Translate(F''', Vector[(-u)]) → T_7
  385. Translate(I_6, Vector[(-u)]) → U_7
  386. PolyLine(G_7, H_7, Q_7, R_7, S_7, T_7, U_7, I_7, J_7, K_7, L_7, M_7, N_7, O_7, P_7) → recht''_1
  387. Translate(D_6, Vector[(-uu)]) → V_7
  388. Translate(F''_1, Vector[(-uu)]) → W_7
  389. Translate(G'_4, Vector[(-uu)]) → Z_7
  390. Translate(F'_3, Vector[(-uu)]) → A_8
  391. Translate(E'_3, Vector[(-uu)]) → B_8
  392. Translate(D'_2, Vector[(-uu)]) → C_8
  393. Translate(E''_1, Vector[(-uu)]) → D_8
  394. Translate(E_6, Vector[(-uu)]) → E_8
  395. Translate(E''', Vector[(-uu)]) → F_8
  396. Translate(F_6, Vector[(-uu)]) → G_8
  397. Translate(G_6, Vector[(-uu)]) → H_8
  398. Translate(H_6, Vector[(-uu)]) → I_8
  399. Translate(G''', Vector[(-uu)]) → J_8
  400. Translate(F''', Vector[(-uu)]) → K_8
  401. Translate(I_6, Vector[(-uu)]) → L_8
  402. PolyLine(V_7, W_7, H_8, I_8, J_8, K_8, L_8, Z_7, A_8, B_8, C_8, D_8, E_8, F_8, G_8) → recht''_2
  403. Translate(D_3, Vector[(-u)]) → M_8
  404. Translate(F', Vector[(-u)]) → F''_3
  405. Translate(G, Vector[(-u)]) → G'_6
  406. Translate(F, Vector[(-u)]) → F'_5
  407. Translate(E, Vector[(-u)]) → E'_5
  408. Translate(D, Vector[(-u)]) → D'_4
  409. Translate(E', Vector[(-u)]) → E''_3
  410. Translate(E_3, Vector[(-u)]) → N_8
  411. Translate(E'', Vector[(-u)]) → E'''_2
  412. Translate(D'_1, Vector[(-u)]) → O_8
  413. Translate(E'_1, Vector[(-u)]) → P_8
  414. Translate(F'_1, Vector[(-u)]) → Q_8
  415. Translate(G'', Vector[(-u)]) → G'''_2
  416. Translate(F'', Vector[(-u)]) → F'''_2
  417. Translate(D_3, Vector[(-u)]) → R_8
  418. PolyLine(M_8, F''_3, P_8, Q_8, G'''_2, F'''_2, R_8, G'_6, F'_5, E'_5, D'_4, E''_3, N_8, E'''_2, O_8) → recht'_2
  419. Translate(D_3, uu) → S_8
  420. Translate(F', uu) → F''_4
  421. Translate(G, uu) → G'_7
  422. Translate(F, uu) → F'_6
  423. Translate(E, uu) → E'_6
  424. Translate(D, uu) → D'_5
  425. Translate(E', uu) → E''_4
  426. Translate(E_3, uu) → T_8
  427. Translate(E'', uu) → E'''_3
  428. Translate(D'_1, uu) → U_8
  429. Translate(E'_1, uu) → V_8
  430. Translate(F'_1, uu) → W_8
  431. Translate(G'', uu) → G'''_3
  432. Translate(F'', uu) → F'''_3
  433. Translate(D_3, uu) → Z_8
  434. PolyLine(S_8, F''_4, V_8, W_8, G'''_3, F'''_3, Z_8, G'_7, F'_6, E'_6, D'_5, E''_4, T_8, E'''_3, U_8) → recht'_3
  435. OrthogonalLine(G, o) → h_5
  436. Point(h_5) → B_9
  437. Polygon(G, O, F) → driehoek1, f_5, g_5, o_3
  438. Segment(O, F) → b_4
  439. Angle(O, G, F) → β
  440. Angle(F, O, G) → α
  441. Angle(G, F, O) → γ
  442. Segment(O, E) → c_4
  443. Segment(O, C) → d_4
  444. Segment(O, B) → e_4
  445. FractionText(1 / 7) → tekst1
  446. Point(h_5) → A_9
  447. Segment(B_9, A_9) → i_5
  448. Point(i_5) → C_9
  449. Circle(C_9, D_9) → c_5
  450. Mirror(F, i_5) → F'_7
  451. Ray(C_9, F'_7) → j_5
  452. Intersect(c_5, j_5, 1) → E_9
  453. Segment(C_9, E_9) → k_5
  454. Mirror(B, i_5) → B'_3
  455. Ray(C_9, B'_3) → l_5
  456. Intersect(c_5, l_5, 1) → F_9
  457. Segment(C_9, F_9) → m_5
  458. Midpoint(i_2) → G_9
  459. Rotate(I, β, G_9) → I'_{10}
  460. Segment(G_9, I'_{10}) → n_5
  461. Midpoint(p) → H_9
  462. Segment(G_9, H_9) → sym
  463. Mirror(G_9, sym) → I_9
  464. Mirror(I'_{10}, sym) → J_9
  465. Segment(I_9, J_9) → p_5
  466. Mirror(C_9, sym) → K_9
  467. Mirror(E_9, sym) → L_9
  468. Segment(K_9, L_9) → q_5
  469. Mirror(F, sym) → F'_8
  470. Mirror(G, sym) → G'_8
  471. Segment(F'_8, G'_8) → k'_4
  472. Mirror(E, sym) → E'_7
  473. Mirror(F, sym) → F'_9
  474. Segment(E'_7, F'_9) → j'_3
  475. Mirror(D, sym) → D'_6
  476. Mirror(E, sym) → E'_8
  477. Segment(D'_6, E'_8) → i'_{12}
  478. Mirror(C_9, xAxis) → M_9
  479. Mirror(E_9, xAxis) → N_9
  480. Segment(M_9, N_9) → r_5
  481. Mirror(G_9, xAxis) → O_9
  482. Mirror(I'_{10}, xAxis) → P_9
  483. Segment(O_9, P_9) → s_5
  484. Mirror(K_9, xAxis) → Q_9
  485. Mirror(L_9, xAxis) → R_9
  486. Segment(Q_9, R_9) → t_5
  487. Mirror(I_9, xAxis) → S_9
  488. Mirror(J_9, xAxis) → T_9
  489. Segment(S_9, T_9) → a_5
  490. Midpoint(i_1) → U_9
  491. Rotate(I, (-β), U_9) → I'_{11}
  492. Circle(U_9, V_9) → d_5
  493. Ray(U_9, I'_{11}) → b_5
  494. Intersect(d_5, b_5, 1) → W_9
  495. Segment(U_9, W_9) → e_5
  496. OrthogonalLine(U_9, i_1) → sym3
  497. Mirror(U_9, sym3) → Z_9
  498. Mirror(W_9, sym3) → A_{10}
  499. Segment(Z_9, A_{10}) → f_6
  500. Segment(K, O) → sym2
  501. Mirror(C_9, sym2) → B_{10}
  502. Mirror(F_9, sym2) → C_{10}
  503. Segment(B_{10}, C_{10}) → g_6
  504. Mirror(U_9, sym2) → D_{10}
  505. Mirror(W_9, sym2) → E_{10}
  506. Segment(D_{10}, E_{10}) → h_6
  507. Mirror(Z_9, sym2) → F_{10}
  508. Mirror(A_{10}, sym2) → G_{10}
  509. Segment(F_{10}, G_{10}) → i_6
  510. Mirror(G, sym3) → G'_9
  511. Mirror(B, sym3) → B'_4
  512. Segment(G'_9, B'_4) → l'_6
  513. Mirror(B, sym3) → B'_5
  514. Mirror(A, sym3) → A'_2
  515. Segment(B'_5, A'_2) → f'
  516. Mirror(B_{10}, sym3) → H_{10}
  517. Mirror(C_{10}, sym3) → I_{10}
  518. Segment(H_{10}, I_{10}) → j_6
  519. Mirror(C_9, sym3) → J_{10}
  520. Mirror(F_9, sym3) → K_{10}
  521. Segment(J_{10}, K_{10}) → k_6

AI Drawing Prompt Reference

Draw an Islamic geometric pattern featuring multiple symmetric polygons created through rotations and mirror transformations. Start by constructing a base polygon, then rotate and mirror it around the center to generate several interconnected shapes. Next, calculate midpoints and vectors, and translate these polygons to form a more complex design. Finally, perform additional rotations and translations to enhance the pattern's richness and symmetry.
The prompt above was compiled from the original drawing commands and is for reference only.