MathPlotAI Logo MathPlotAI

Islamic Geometric Pattern with 10/4 Polygons

Islamic Geometric Pattern with 10/4 Polygons
Loading the math board and drawing, please wait…
2019-12-31 16:27
PolygonSequenceTransformationGeometric Construction
This GeoGebra example demonstrates the construction of an Islamic-style geometric pattern based on 10/4 polygons, where a decagon is rotated by 4 vertices each step, creating a periodic tiling with rich symmetry. The core mathematical concepts include polygon symmetry, rotational and mirror symmetry, special points on the unit circle, median lines, hyperbolas, and the sine function's role in pattern generation. The construction uses GeoGebra commands such as Rotate, Polygon, Segment, Midpoint, Intersect, PolyLine, Mirror, Sequence, Centroid, Vector, and Translate to build the intricate design. It is suitable for high school and above, serving as an excellent resource for exploring geometric transformations, symmetry groups, and the mathematical foundations of Islamic art, as well as for interdisciplinary STEAM education.

GeoGebra Commands & Parameters

  1. ConstructionStep() → stap
  2. Rotate(A, 36°) → B
  3. Polygon(A, B, 10) → veelhoek1, f, p, C, D, E, F, G, H, I, J, g, h, i, j, k, l, m, n
  4. Polygon(A, J, 5) → veelhoek2, q, r, s, t, a, K, L, M
  5. Polygon(B, A, 5) → veelhoek3, b, c, d, e, f_1, N, P, Q
  6. Polygon(C, B, 5) → veelhoek4, g_1, h_1, i_1, j_1, k_1, R, S, T
  7. Polygon(E, D, 5) → veelhoek6, r_1, s_1, t_1, a_1, b_1, Z, A_1, B_1
  8. Polygon(F, E, 5) → veelhoek7, c_1, d_1, e_1, f_2, g_2, C_1, D_1, E_1
  9. Polygon(G, F, 5) → veelhoek8, h_2, i_2, j_2, k_2, l_2, F_1, G_1, H_1
  10. Polygon(H, G, 5) → veelhoek9, m_2, n_2, p_2, q_2, r_2, I_1, J_1, K_1
  11. Polygon(J, I, 5) → veelhoek11, d_2, e_2, f_3, g_3, h_3, O_1, P_1, Q_1
  12. Polygon(D_1, B_1, 10) → veelhoek12, i_3, s_3, R_1, S_1, T_1, U_1, V_1, W_1, Z_1, A_2, j_3, k_3, l_3, m_3, n_3, p_3, q_3, r_3
  13. Polygon(J_1, H_1, 10) → veelhoek13, t_3, i_4, B_2, C_2, D_2, E_2, F_2, G_2, H_2, I_2, a_3, b_3, c_3, d_3, e_3, f_4, g_4, h_4
  14. Polygon(S_1, A_1, 5) → veelhoek14, j_4, k_4, l_4, m_4, n_4, J_2, K_2, L_2
  15. Polygon(T_1, S_1, 5) → veelhoek15, p_4, q_4, r_4, s_4, t_4, M_2, N_2, O_2
  16. Polygon(N_2, L_2, 10) → veelhoek16, a_4, j_5, P_2, Q_2, R_2, S_2, T_2, U_2, V_2, W_2, b_4, c_4, d_4, e_4, f_5, g_5, h_5, i_5
  17. Polygon(Q_2, T, 5) → veelhoek5, l_1, m_1, n_1, p_1, q_1, U, V, W
  18. Polygon(A_2, Z_1, 5) → veelhoek10, s_2, t_2, a_2, b_2, c_2, L_1, M_1, N_1
  19. Polygon(D_2, C_2, 5) → veelhoek17, k_5, l_5, m_5, n_5, p_5, Z_2, A_3, B_3
  20. Polygon(Z_1, W_1, 5) → veelhoek18, q_5, r_5, s_5, t_5, a_5, C_3, D_3, E_3
  21. Polygon(E_2, D_2, 5) → veelhoek19, b_5, c_5, d_5, e_5, f_6, F_3, G_3, H_3
  22. Polygon(J_1, I_2, 5) → veelhoek20, g_6, h_6, i_6, j_6, k_6, I_3, J_3, K_3
  23. Polygon(P_1, O_1, 5) → veelhoek21, l_6, m_6, n_6, p_6, q_6, L_3, M_3, N_3
  24. Polygon(K, P_1, 10) → veelhoek22, r_6, g_7, O_3, P_3, Q_3, R_3, S_3, T_3, U_3, V_3, s_6, t_6, a_6, b_6, c_6, d_6, e_6, f_7
  25. Polygon(V, S, 10) → veelhoek23, h_7, r_7, W_3, Z_3, A_4, B_4, C_4, D_4, E_4, F_4, i_7, j_7, k_7, l_7, m_7, n_7, p_7, q_7
  26. Polygon(S_2, R_2, 5) → veelhoek24, s_7, t_7, a_7, b_7, c_7, G_4, H_4, I_4
  27. Polygon(T_2, S_2, 5) → veelhoek25, d_7, e_7, f_8, g_8, h_8, J_4, K_4, L_4
  28. Polygon(N_2, W_2, 5) → veelhoek26, i_8, j_8, k_8, l_8, m_8, M_4, N_4, O_4
  29. Polygon(V_1, U_1, 5) → veelhoek27, n_8, p_8, q_8, r_8, s_8, P_4, Q_4, R_4
  30. Polygon(W_1, V_1, 5) → veelhoek28, t_8, a_8, b_8, c_8, d_8, S_4, T_4, U_4
  31. Polygon(B_3, M_1, 10) → veelhoek29, e_8, n_9, V_4, W_4, Z_4, A_5, B_5, C_5, D_5, E_5, f_9, g_9, h_9, i_9, j_9, k_9, l_9, m_9
  32. Polygon(F_2, E_2, 5) → veelhoek30, p_9, q_9, r_9, s_9, t_9, F_5, G_5, H_5
  33. Polygon(Q_4, P_4, 5) → veelhoek31, a_9, b_9, c_9, d_9, e_9, I_5, J_5, K_5
  34. Polygon(R_4, Q_4, 10) → veelhoek32, f_{10}, p_{10}, L_5, M_5, N_5, O_5, P_5, Q_5, R_5, S_5, g_{10}, h_{10}, i_{10}, j_{10}, k_{10}, l_{10}, m_{10}, n_{10}
  35. Polygon(U_3, T_3, 5) → veelhoek33, q_{10}, r_{10}, s_{10}, t_{10}, a_{10}, T_5, U_5, V_5
  36. Polygon(A_4, V_5, 5) → veelhoek34, b_{10}, c_{10}, d_{10}, e_{10}, f_{11}, W_5, Z_5, A_6
  37. Polygon(E_4, D_4, 5) → veelhoek35, g_{11}, h_{11}, i_{11}, j_{11}, k_{11}, B_6, C_6, D_6
  38. Polygon(D_5, C_5, 5) → veelhoek36, l_{11}, m_{11}, n_{11}, p_{11}, q_{11}, E_6, F_6, G_6
  39. Polygon(R_5, Q_5, 5) → veelhoek37, r_{11}, s_{11}, t_{11}, a_{11}, b_{11}, H_6, I_6, J_6
  40. Polygon(A_5, Z_4, 5) → veelhoek38, c_{11}, d_{11}, e_{11}, f_{12}, g_{12}, K_6, L_6, M_6
  41. Polygon(G_6, F_6, 5) → veelhoek39, h_{12}, i_{12}, j_{12}, k_{12}, l_{12}, N_6, O_6, P_6
  42. Segment(P_6, G_5) → m_{12}
  43. Segment(J_3, L_3) → n_{12}
  44. Polygon(T_3, S_3, 5) → veelhoek40, p_{12}, q_{12}, r_{12}, s_{12}, t_{12}, Q_6, R_6, S_6
  45. Polygon(S_3, R_3, 5) → veelhoek41, a_{12}, b_{12}, c_{12}, d_{12}, e_{12}, T_6, U_6, V_6
  46. Polygon(C_4, B_4, 5) → veelhoek42, f_{13}, g_{13}, h_{13}, i_{13}, j_{13}, W_6, Z_6, A_7
  47. Polygon(D_4, C_4, 5) → veelhoek43, k_{13}, l_{13}, m_{13}, n_{13}, p_{13}, B_7, C_7, D_7
  48. Polygon(D_6, C_6, 5) → veelhoek44, q_{13}, r_{13}, s_{13}, t_{13}, a_{13}, E_7, F_7, G_7
  49. Segment(K_4, G_7) → b_{13}
  50. Segment(I_5, N_4) → c_{13}
  51. Midpoint(k) → H_7
  52. Midpoint(p) → I_7
  53. Midpoint(l) → J_7
  54. Midpoint(m) → K_7
  55. Midpoint(n) → L_7
  56. Midpoint(f) → M_7
  57. Midpoint(g) → N_7
  58. Midpoint(h) → O_7
  59. Midpoint(i) → P_7
  60. Midpoint(j) → Q_7
  61. Segment(H_7, I_7) → d_{13}
  62. Segment(J_7, M_7) → e_{13}
  63. Segment(K_7, N_7) → f_{14}
  64. Segment(L_7, O_7) → g_{14}
  65. Segment(I_7, P_7) → h_{14}
  66. Segment(M_7, Q_7) → i_{14}
  67. Segment(N_7, H_7) → j_{14}
  68. Segment(O_7, J_7) → k_{14}
  69. Segment(P_7, K_7) → l_{14}
  70. Segment(Q_7, L_7) → m_{14}
  71. Intersect(j_{14}, m_{14}) → R_7
  72. Intersect(d_{13}, k_{14}) → S_7
  73. Intersect(e_{13}, l_{14}) → T_7
  74. Intersect(f_{14}, m_{14}) → U_7
  75. Intersect(d_{13}, g_{14}) → V_7
  76. Intersect(e_{13}, h_{14}) → W_7
  77. Intersect(f_{14}, i_{14}) → Z_7
  78. Intersect(g_{14}, j_{14}) → A_8
  79. Intersect(h_{14}, k_{14}) → B_8
  80. Intersect(i_{14}, l_{14}) → C_8
  81. Intersect(k_{14}, m_{14}) → D_8
  82. Intersect(e_{13}, m_{14}) → E_8
  83. Intersect(d_{13}, f_{14}) → F_8
  84. Intersect(e_{13}, g_{14}) → G_8
  85. Intersect(g_{14}, i_{14}) → H_8
  86. Intersect(j_{14}, l_{14}) → J_8
  87. Intersect(f_{14}, h_{14}) → I_8
  88. Intersect(h_{14}, j_{14}) → K_8
  89. Intersect(i_{14}, k_{14}) → L_8
  90. Intersect(d_{13}, l_{14}) → M_8
  91. PolyLine(R_7, D_8, W_7, I_8, Z_7, H_8, A_8, K_8, B_8, L_8, C_8, J_8, S_7, R_7, M_8, T_7, E_8, U_7, F_8, V_7, G_8) → sterbi
  92. PolyLine(Q_7, R_7, I_7, W_7, M_7, Z_7, N_7, A_8, O_7, B_8, P_7, C_8, H_7, Q_7, S_7, J_7, T_7, K_7, U_7, L_7, V_7) → sterbu
  93. Intersect(g_2, i_2) → N_8
  94. Midpoint(g_2) → O_8
  95. Rotate(N_8, 72°, O_8) → P_8
  96. Mirror(P_8, yAxis) → Q_8
  97. Polygon(R_7, Q_7, P_8, O_8, Q_8, H_7) → roos, q_{14}, r_{14}, s_{14}, o_8, t_{14}, a_{14}
  98. Sequence(Polygon[Rotate[R_7, (nn * 36°)], Rotate[Q_7, (nn * 36°)], Rotate[P_8, (nn * 36°)], Rotate[O_8, (nn * 36°)], Rotate[Q_8, (nn * 36°)], Rotate[H_7, (nn * 36°)]], nn, 1, 10) → roosrij
  99. Centroid(veelhoek16) → R_8
  100. Vector(O, R_8) → u
  101. Centroid(veelhoek12) → S_8
  102. Centroid(veelhoek23) → T_8
  103. Centroid(veelhoek29) → U_8
  104. Vector(O, S_8) → v
  105. Vector(O, U_8) → w
  106. Vector(O, T_8) → u_1
  107. Translate(R_7, u) → V_8
  108. Translate(D_8, u) → W_8
  109. Translate(S_7, u) → Z_8
  110. Translate(M_8, u) → A_9
  111. Translate(T_7, u) → B_9
  112. Translate(E_8, u) → C_9
  113. Translate(U_7, u) → D_9
  114. Translate(F_8, u) → E_9
  115. Translate(V_7, u) → F_9
  116. Translate(G_8, u) → G_9
  117. Translate(W_7, u) → H_9
  118. Translate(I_8, u) → I_9
  119. Translate(Z_7, u) → J_9
  120. Translate(H_8, u) → K_9
  121. Translate(A_8, u) → L_9
  122. Translate(K_8, u) → M_9
  123. Translate(B_8, u) → N_9
  124. Translate(L_8, u) → O_9
  125. Translate(C_8, u) → P_9
  126. Translate(J_8, u) → Q_9
  127. Translate(R_7, u) → R_9
  128. PolyLine(V_8, W_8, H_9, I_9, J_9, K_9, L_9, M_9, N_9, O_9, P_9, Q_9, Z_8, R_9, A_9, B_9, C_9, D_9, E_9, F_9, G_9) → sterbi'
  129. Translate(Q_7, u) → S_9
  130. Translate(R_7, u) → T_9
  131. Translate(H_7, u) → U_9
  132. Translate(S_7, u) → V_9
  133. Translate(J_7, u) → W_9
  134. Translate(T_7, u) → Z_9
  135. Translate(K_7, u) → A_{10}
  136. Translate(U_7, u) → B_{10}
  137. Translate(L_7, u) → C_{10}
  138. Translate(V_7, u) → D_{10}
  139. Translate(I_7, u) → E_{10}
  140. Translate(W_7, u) → F_{10}
  141. Translate(M_7, u) → G_{10}
  142. Translate(Z_7, u) → H_{10}
  143. Translate(N_7, u) → I_{10}
  144. Translate(A_8, u) → J_{10}
  145. Translate(O_7, u) → K_{10}
  146. Translate(B_8, u) → L_{10}
  147. Translate(P_7, u) → M_{10}
  148. Translate(C_8, u) → N_{10}
  149. Translate(Q_7, u) → O_{10}
  150. PolyLine(S_9, T_9, E_{10}, F_{10}, G_{10}, H_{10}, I_{10}, J_{10}, K_{10}, L_{10}, M_{10}, N_{10}, U_9, O_{10}, V_9, W_9, Z_9, A_{10}, B_{10}, C_{10}, D_{10}) → sterbu'
  151. Translate(roosrij, u) → roosrij'
  152. Translate(R_7, u_1) → P_{10}
  153. Translate(D_8, u_1) → Q_{10}
  154. Translate(S_7, u_1) → R_{10}
  155. Translate(M_8, u_1) → S_{10}
  156. Translate(T_7, u_1) → T_{10}
  157. Translate(E_8, u_1) → U_{10}
  158. Translate(U_7, u_1) → V_{10}
  159. Translate(F_8, u_1) → W_{10}
  160. Translate(V_7, u_1) → Z_{10}
  161. Translate(G_8, u_1) → A_{11}
  162. Translate(W_7, u_1) → B_{11}
  163. Translate(I_8, u_1) → C_{11}
  164. Translate(Z_7, u_1) → D_{11}
  165. Translate(H_8, u_1) → E_{11}
  166. Translate(A_8, u_1) → F_{11}
  167. Translate(K_8, u_1) → G_{11}
  168. Translate(B_8, u_1) → H_{11}
  169. Translate(L_8, u_1) → I_{11}
  170. Translate(C_8, u_1) → J_{11}
  171. Translate(J_8, u_1) → K_{11}
  172. Translate(R_7, u_1) → L_{11}
  173. PolyLine(P_{10}, Q_{10}, B_{11}, C_{11}, D_{11}, E_{11}, F_{11}, G_{11}, H_{11}, I_{11}, J_{11}, K_{11}, R_{10}, L_{11}, S_{10}, T_{10}, U_{10}, V_{10}, W_{10}, Z_{10}, A_{11}) → sterbi'_1
  174. Translate(Q_7, u_1) → M_{11}
  175. Translate(R_7, u_1) → N_{11}
  176. Translate(H_7, u_1) → O_{11}
  177. Translate(S_7, u_1) → P_{11}
  178. Translate(J_7, u_1) → Q_{11}
  179. Translate(T_7, u_1) → R_{11}
  180. Translate(K_7, u_1) → S_{11}
  181. Translate(U_7, u_1) → T_{11}
  182. Translate(L_7, u_1) → U_{11}
  183. Translate(V_7, u_1) → V_{11}
  184. Translate(I_7, u_1) → W_{11}
  185. Translate(W_7, u_1) → Z_{11}
  186. Translate(M_7, u_1) → A_{12}
  187. Translate(Z_7, u_1) → B_{12}
  188. Translate(N_7, u_1) → C_{12}
  189. Translate(A_8, u_1) → D_{12}
  190. Translate(O_7, u_1) → E_{12}
  191. Translate(B_8, u_1) → F_{12}
  192. Translate(P_7, u_1) → G_{12}
  193. Translate(C_8, u_1) → H_{12}
  194. Translate(Q_7, u_1) → I_{12}
  195. PolyLine(M_{11}, N_{11}, W_{11}, Z_{11}, A_{12}, B_{12}, C_{12}, D_{12}, E_{12}, F_{12}, G_{12}, H_{12}, O_{11}, I_{12}, P_{11}, Q_{11}, R_{11}, S_{11}, T_{11}, U_{11}, V_{11}) → sterbu'_1
  196. Translate(roosrij, u_1) → roosrij'_1
  197. Translate(R_7, Vector[(-v)]) → J_{12}
  198. Translate(D_8, Vector[(-v)]) → K_{12}
  199. Translate(S_7, Vector[(-v)]) → L_{12}
  200. Translate(M_8, Vector[(-v)]) → M_{12}
  201. Translate(T_7, Vector[(-v)]) → N_{12}
  202. Translate(E_8, Vector[(-v)]) → O_{12}
  203. Translate(U_7, Vector[(-v)]) → P_{12}
  204. Translate(F_8, Vector[(-v)]) → Q_{12}
  205. Translate(V_7, Vector[(-v)]) → R_{12}
  206. Translate(G_8, Vector[(-v)]) → S_{12}
  207. Translate(W_7, Vector[(-v)]) → T_{12}
  208. Translate(I_8, Vector[(-v)]) → U_{12}
  209. Translate(Z_7, Vector[(-v)]) → V_{12}
  210. Translate(H_8, Vector[(-v)]) → W_{12}
  211. Translate(A_8, Vector[(-v)]) → Z_{12}
  212. Translate(K_8, Vector[(-v)]) → A_{13}
  213. Translate(B_8, Vector[(-v)]) → B_{13}
  214. Translate(L_8, Vector[(-v)]) → C_{13}
  215. Translate(C_8, Vector[(-v)]) → D_{13}
  216. Translate(J_8, Vector[(-v)]) → E_{13}
  217. Translate(R_7, Vector[(-v)]) → F_{13}
  218. PolyLine(J_{12}, K_{12}, T_{12}, U_{12}, V_{12}, W_{12}, Z_{12}, A_{13}, B_{13}, C_{13}, D_{13}, E_{13}, L_{12}, F_{13}, M_{12}, N_{12}, O_{12}, P_{12}, Q_{12}, R_{12}, S_{12}) → sterbi'_2
  219. Translate(Q_7, Vector[(-v)]) → G_{13}
  220. Translate(R_7, Vector[(-v)]) → H_{13}
  221. Translate(H_7, Vector[(-v)]) → I_{13}
  222. Translate(S_7, Vector[(-v)]) → J_{13}
  223. Translate(J_7, Vector[(-v)]) → K_{13}
  224. Translate(T_7, Vector[(-v)]) → L_{13}
  225. Translate(K_7, Vector[(-v)]) → M_{13}
  226. Translate(U_7, Vector[(-v)]) → N_{13}
  227. Translate(L_7, Vector[(-v)]) → O_{13}
  228. Translate(V_7, Vector[(-v)]) → P_{13}
  229. Translate(I_7, Vector[(-v)]) → Q_{13}
  230. Translate(W_7, Vector[(-v)]) → R_{13}
  231. Translate(M_7, Vector[(-v)]) → S_{13}
  232. Translate(Z_7, Vector[(-v)]) → T_{13}
  233. Translate(N_7, Vector[(-v)]) → U_{13}
  234. Translate(A_8, Vector[(-v)]) → V_{13}
  235. Translate(O_7, Vector[(-v)]) → W_{13}
  236. Translate(B_8, Vector[(-v)]) → Z_{13}
  237. Translate(P_7, Vector[(-v)]) → A_{14}
  238. Translate(C_8, Vector[(-v)]) → B_{14}
  239. Translate(Q_7, Vector[(-v)]) → C_{14}
  240. PolyLine(G_{13}, 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}) → sterbu'_2
  241. Translate(roosrij, Vector[(-v)]) → roosrij'_2
  242. Mirror(R_7, O_8) → D_{14}
  243. Mirror(Q_7, O_8) → E_{14}
  244. Mirror(P_8, O_8) → F_{14}
  245. Mirror(O_8, O_8) → G_{14}
  246. Mirror(Q_8, O_8) → H_{14}
  247. Mirror(H_7, O_8) → I_{14}
  248. Polygon(D_{14}, E_{14}, F_{14}, G_{14}, H_{14}, I_{14}) → roos', d_{14}, e_{14}, n_{14}, p_{14}, b_{14}, c_{14}
  249. Mirror(D_{14}, xAxis) → J_{14}
  250. Mirror(E_{14}, xAxis) → K_{14}
  251. Mirror(F_{14}, xAxis) → L_{14}
  252. Mirror(G_{14}, xAxis) → M_{14}
  253. Mirror(H_{14}, xAxis) → N_{14}
  254. Mirror(I_{14}, xAxis) → O_{14}
  255. Polygon(J_{14}, K_{14}, L_{14}, M_{14}, N_{14}, O_{14}) → roos'', f_{15}, g_{15}, h_{15}, i_{15}, j_{15}, o_{14}
  256. Translate(J_{14}, v) → P_{14}
  257. Translate(K_{14}, v) → Q_{14}
  258. Translate(L_{14}, v) → R_{14}
  259. Translate(M_{14}, v) → S_{14}
  260. Translate(N_{14}, v) → T_{14}
  261. Translate(O_{14}, v) → U_{14}
  262. Polygon(P_{14}, Q_{14}, R_{14}, S_{14}, T_{14}, U_{14}) → roos''', k_{15}, l_{15}, m_{15}, n_{15}, p_{15}, u_{14}
  263. Translate(D_{14}, u_1) → V_{14}
  264. Translate(E_{14}, u_1) → W_{14}
  265. Translate(F_{14}, u_1) → Z_{14}
  266. Translate(G_{14}, u_1) → A_{15}
  267. Translate(H_{14}, u_1) → B_{15}
  268. Translate(I_{14}, u_1) → C_{15}
  269. Polygon(V_{14}, W_{14}, Z_{14}, A_{15}, B_{15}, C_{15}) → roos''_1, v_{14}, w_{14}, z_{14}, a_{15}, b_{15}, c_{15}
  270. Translate(D_{14}, Vector[(-v)]) → D_{15}
  271. Translate(E_{14}, Vector[(-v)]) → E_{15}
  272. Translate(F_{14}, Vector[(-v)]) → F_{15}
  273. Translate(G_{14}, Vector[(-v)]) → G_{15}
  274. Translate(H_{14}, Vector[(-v)]) → H_{15}
  275. Translate(I_{14}, Vector[(-v)]) → I_{15}
  276. Polygon(D_{15}, E_{15}, F_{15}, G_{15}, H_{15}, I_{15}) → roos''_2, d_{15}, e_{15}, q_{15}, r_{15}, s_{15}, t_{15}
  277. Translate(J_{14}, Vector[(-u_1)]) → J_{15}
  278. Translate(K_{14}, Vector[(-u_1)]) → K_{15}
  279. Translate(L_{14}, Vector[(-u_1)]) → L_{15}
  280. Translate(M_{14}, Vector[(-u_1)]) → M_{15}
  281. Translate(N_{14}, Vector[(-u_1)]) → N_{15}
  282. Translate(O_{14}, Vector[(-u_1)]) → O_{15}
  283. Polygon(J_{15}, K_{15}, L_{15}, M_{15}, N_{15}, O_{15}) → roos'''_1, f_{16}, g_{16}, h_{16}, i_{16}, j_{16}, o_{15}
  284. Translate(D_{14}, u) → P_{15}
  285. Translate(E_{14}, u) → Q_{15}
  286. Translate(F_{14}, u) → R_{15}
  287. Translate(G_{14}, u) → S_{15}
  288. Translate(H_{14}, u) → T_{15}
  289. Translate(I_{14}, u) → U_{15}
  290. Polygon(P_{15}, Q_{15}, R_{15}, S_{15}, T_{15}, U_{15}) → roos''_3, k_{16}, l_{16}, m_{16}, n_{16}, p_{16}, u_{15}
  291. Translate(J_{14}, Vector[(2 * v)]) → V_{15}
  292. Translate(K_{14}, Vector[(2 * v)]) → W_{15}
  293. Translate(L_{14}, Vector[(2 * v)]) → Z_{15}
  294. Translate(M_{14}, Vector[(2 * v)]) → A_{16}
  295. Translate(N_{14}, Vector[(2 * v)]) → B_{16}
  296. Translate(O_{14}, Vector[(2 * v)]) → C_{16}
  297. Polygon(V_{15}, W_{15}, Z_{15}, A_{16}, B_{16}, C_{16}) → roos'''_2, v_{15}, w_{15}, z_{15}, a_{16}, b_{16}, c_{16}
  298. Translate(J_{14}, w) → D_{16}
  299. Translate(K_{14}, w) → E_{16}
  300. Translate(L_{14}, w) → F_{16}
  301. Translate(M_{14}, w) → G_{16}
  302. Translate(N_{14}, w) → H_{16}
  303. Translate(O_{14}, w) → I_{16}
  304. Polygon(D_{16}, E_{16}, F_{16}, G_{16}, H_{16}, I_{16}) → roos'''_3, d_{16}, e_{16}, q_{16}, r_{16}, s_{16}, t_{16}
  305. Translate(D_{14}, Vector[(-u_1)]) → J_{16}
  306. Translate(E_{14}, Vector[(-u_1)]) → K_{16}
  307. Translate(F_{14}, Vector[(-u_1)]) → L_{16}
  308. Translate(G_{14}, Vector[(-u_1)]) → M_{16}
  309. Translate(H_{14}, Vector[(-u_1)]) → N_{16}
  310. Translate(I_{14}, Vector[(-u_1)]) → O_{16}
  311. Polygon(J_{16}, K_{16}, L_{16}, M_{16}, N_{16}, O_{16}) → roos''_4, f_{17}, g_{17}, h_{17}, i_{17}, j_{17}, o_{16}
  312. Translate(D_{14}, v) → P_{16}
  313. Translate(E_{14}, v) → Q_{16}
  314. Translate(F_{14}, v) → R_{16}
  315. Translate(G_{14}, v) → S_{16}
  316. Translate(H_{14}, v) → T_{16}
  317. Translate(I_{14}, v) → U_{16}
  318. Polygon(P_{16}, Q_{16}, R_{16}, S_{16}, T_{16}, U_{16}) → roos''_5, k_{17}, l_{17}, m_{17}, n_{17}, p_{17}, u_{16}
  319. Translate(D_{14}, Vector[(2 * u_1)]) → V_{16}
  320. Translate(E_{14}, Vector[(2 * u_1)]) → W_{16}
  321. Translate(F_{14}, Vector[(2 * u_1)]) → Z_{16}
  322. Translate(G_{14}, Vector[(2 * u_1)]) → A_{17}
  323. Translate(H_{14}, Vector[(2 * u_1)]) → B_{17}
  324. Translate(I_{14}, Vector[(2 * u_1)]) → C_{17}
  325. Polygon(V_{16}, W_{16}, Z_{16}, A_{17}, B_{17}, C_{17}) → roos''_6, v_{16}, w_{16}, z_{16}, a_{17}, b_{17}, c_{17}
  326. Translate(J_{14}, u) → D_{17}
  327. Translate(K_{14}, u) → E_{17}
  328. Translate(L_{14}, u) → F_{17}
  329. Translate(M_{14}, u) → G_{17}
  330. Translate(N_{14}, u) → H_{17}
  331. Translate(O_{14}, u) → I_{17}
  332. Polygon(D_{17}, E_{17}, F_{17}, G_{17}, H_{17}, I_{17}) → roos'''_4, d_{17}, e_{17}, q_{17}, r_{17}, s_{17}, t_{17}
  333. Translate(V_{16}, Vector[(-u)]) → J_{17}
  334. Translate(W_{16}, Vector[(-u)]) → K_{17}
  335. Translate(Z_{16}, Vector[(-u)]) → L_{17}
  336. Translate(A_{17}, Vector[(-u)]) → M_{17}
  337. Translate(B_{17}, Vector[(-u)]) → N_{17}
  338. Translate(C_{17}, Vector[(-u)]) → O_{17}
  339. Polygon(J_{17}, K_{17}, L_{17}, M_{17}, N_{17}, O_{17}) → veelhoek45, f_{18}, g_{18}, h_{18}, i_{18}, j_{18}, o_{17}
  340. Translate(D_{16}, v) → P_{17}
  341. Translate(E_{16}, v) → Q_{17}
  342. Translate(F_{16}, v) → R_{17}
  343. Translate(G_{16}, v) → S_{17}
  344. Translate(H_{16}, v) → T_{17}
  345. Translate(I_{16}, v) → U_{17}
  346. Polygon(P_{17}, Q_{17}, R_{17}, S_{17}, T_{17}, U_{17}) → veelhoek46, k_{18}, l_{18}, m_{18}, n_{18}, p_{18}, u_{17}
  347. Translate(D_{16}, Vector[(-u_1)]) → V_{17}
  348. Translate(E_{16}, Vector[(-u_1)]) → W_{17}
  349. Translate(F_{16}, Vector[(-u_1)]) → Z_{17}
  350. Translate(G_{16}, Vector[(-u_1)]) → A_{18}
  351. Translate(H_{16}, Vector[(-u_1)]) → B_{18}
  352. Translate(I_{16}, Vector[(-u_1)]) → C_{18}
  353. Polygon(V_{17}, W_{17}, Z_{17}, A_{18}, B_{18}, C_{18}) → veelhoek47, v_{17}, w_{17}, z_{17}, a_{18}, b_{18}, c_{18}
  354. Translate(R_7, Vector[(-u_1)]) → D_{18}
  355. Translate(D_8, Vector[(-u_1)]) → E_{18}
  356. Translate(S_7, Vector[(-u_1)]) → F_{18}
  357. Translate(M_8, Vector[(-u_1)]) → G_{18}
  358. Translate(T_7, Vector[(-u_1)]) → H_{18}
  359. Translate(E_8, Vector[(-u_1)]) → I_{18}
  360. Translate(U_7, Vector[(-u_1)]) → J_{18}
  361. Translate(F_8, Vector[(-u_1)]) → K_{18}
  362. Translate(V_7, Vector[(-u_1)]) → L_{18}
  363. Translate(G_8, Vector[(-u_1)]) → M_{18}
  364. Translate(W_7, Vector[(-u_1)]) → N_{18}
  365. Translate(I_8, Vector[(-u_1)]) → O_{18}
  366. Translate(Z_7, Vector[(-u_1)]) → P_{18}
  367. Translate(H_8, Vector[(-u_1)]) → Q_{18}
  368. Translate(A_8, Vector[(-u_1)]) → R_{18}
  369. Translate(K_8, Vector[(-u_1)]) → S_{18}
  370. Translate(B_8, Vector[(-u_1)]) → T_{18}
  371. Translate(L_8, Vector[(-u_1)]) → U_{18}
  372. Translate(C_8, Vector[(-u_1)]) → V_{18}
  373. Translate(J_8, Vector[(-u_1)]) → W_{18}
  374. Translate(R_7, Vector[(-u_1)]) → Z_{18}
  375. PolyLine(D_{18}, E_{18}, N_{18}, O_{18}, P_{18}, Q_{18}, R_{18}, S_{18}, T_{18}, U_{18}, V_{18}, W_{18}, F_{18}, Z_{18}, G_{18}, H_{18}, I_{18}, J_{18}, K_{18}, L_{18}, M_{18}) → sterbi'_3
  376. Translate(Q_7, Vector[(-u_1)]) → A_{19}
  377. Translate(R_7, Vector[(-u_1)]) → B_{19}
  378. Translate(H_7, Vector[(-u_1)]) → C_{19}
  379. Translate(S_7, Vector[(-u_1)]) → D_{19}
  380. Translate(J_7, Vector[(-u_1)]) → E_{19}
  381. Translate(T_7, Vector[(-u_1)]) → F_{19}
  382. Translate(K_7, Vector[(-u_1)]) → G_{19}
  383. Translate(U_7, Vector[(-u_1)]) → H_{19}
  384. Translate(L_7, Vector[(-u_1)]) → I_{19}
  385. Translate(V_7, Vector[(-u_1)]) → J_{19}
  386. Translate(I_7, Vector[(-u_1)]) → K_{19}
  387. Translate(W_7, Vector[(-u_1)]) → L_{19}
  388. Translate(M_7, Vector[(-u_1)]) → M_{19}
  389. Translate(Z_7, Vector[(-u_1)]) → N_{19}
  390. Translate(N_7, Vector[(-u_1)]) → O_{19}
  391. Translate(A_8, Vector[(-u_1)]) → P_{19}
  392. Translate(O_7, Vector[(-u_1)]) → Q_{19}
  393. Translate(B_8, Vector[(-u_1)]) → R_{19}
  394. Translate(P_7, Vector[(-u_1)]) → S_{19}
  395. Translate(C_8, Vector[(-u_1)]) → T_{19}
  396. Translate(Q_7, Vector[(-u_1)]) → U_{19}
  397. PolyLine(A_{19}, B_{19}, K_{19}, L_{19}, M_{19}, N_{19}, O_{19}, P_{19}, Q_{19}, R_{19}, S_{19}, T_{19}, C_{19}, U_{19}, D_{19}, E_{19}, F_{19}, G_{19}, H_{19}, I_{19}, J_{19}) → sterbu'_3
  398. Translate(roosrij, Vector[(-u_1)]) → roosrij'_3
  399. Translate(R_7, v) → V_{19}
  400. Translate(D_8, v) → W_{19}
  401. Translate(S_7, v) → Z_{19}
  402. Translate(M_8, v) → A_{20}
  403. Translate(T_7, v) → B_{20}
  404. Translate(E_8, v) → C_{20}
  405. Translate(U_7, v) → D_{20}
  406. Translate(F_8, v) → E_{20}
  407. Translate(V_7, v) → F_{20}
  408. Translate(G_8, v) → G_{20}
  409. Translate(W_7, v) → H_{20}
  410. Translate(I_8, v) → I_{20}
  411. Translate(Z_7, v) → J_{20}
  412. Translate(H_8, v) → K_{20}
  413. Translate(A_8, v) → L_{20}
  414. Translate(K_8, v) → M_{20}
  415. Translate(B_8, v) → N_{20}
  416. Translate(L_8, v) → O_{20}
  417. Translate(C_8, v) → P_{20}
  418. Translate(J_8, v) → Q_{20}
  419. Translate(R_7, v) → R_{20}
  420. PolyLine(V_{19}, W_{19}, H_{20}, I_{20}, J_{20}, K_{20}, L_{20}, M_{20}, N_{20}, O_{20}, P_{20}, Q_{20}, Z_{19}, R_{20}, A_{20}, B_{20}, C_{20}, D_{20}, E_{20}, F_{20}, G_{20}) → sterbi'_4
  421. Translate(Q_7, v) → S_{20}
  422. Translate(R_7, v) → T_{20}
  423. Translate(H_7, v) → U_{20}
  424. Translate(S_7, v) → V_{20}
  425. Translate(J_7, v) → W_{20}
  426. Translate(T_7, v) → Z_{20}
  427. Translate(K_7, v) → A_{21}
  428. Translate(U_7, v) → B_{21}
  429. Translate(L_7, v) → C_{21}
  430. Translate(V_7, v) → D_{21}
  431. Translate(I_7, v) → E_{21}
  432. Translate(W_7, v) → F_{21}
  433. Translate(M_7, v) → G_{21}
  434. Translate(Z_7, v) → H_{21}
  435. Translate(N_7, v) → I_{21}
  436. Translate(A_8, v) → J_{21}
  437. Translate(O_7, v) → K_{21}
  438. Translate(B_8, v) → L_{21}
  439. Translate(P_7, v) → M_{21}
  440. Translate(C_8, v) → N_{21}
  441. Translate(Q_7, v) → O_{21}
  442. PolyLine(S_{20}, T_{20}, E_{21}, F_{21}, G_{21}, H_{21}, I_{21}, J_{21}, K_{21}, L_{21}, M_{21}, N_{21}, U_{20}, O_{21}, V_{20}, W_{20}, Z_{20}, A_{21}, B_{21}, C_{21}, D_{21}) → sterbu'_4
  443. Translate(roosrij, v) → roosrij'_4
  444. Translate(R_7, w) → P_{21}
  445. Translate(D_8, w) → Q_{21}
  446. Translate(S_7, w) → R_{21}
  447. Translate(M_8, w) → S_{21}
  448. Translate(T_7, w) → T_{21}
  449. Translate(E_8, w) → U_{21}
  450. Translate(U_7, w) → V_{21}
  451. Translate(F_8, w) → W_{21}
  452. Translate(V_7, w) → Z_{21}
  453. Translate(G_8, w) → A_{22}
  454. Translate(W_7, w) → B_{22}
  455. Translate(I_8, w) → C_{22}
  456. Translate(Z_7, w) → D_{22}
  457. Translate(H_8, w) → E_{22}
  458. Translate(A_8, w) → F_{22}
  459. Translate(K_8, w) → G_{22}
  460. Translate(B_8, w) → H_{22}
  461. Translate(L_8, w) → I_{22}
  462. Translate(C_8, w) → J_{22}
  463. Translate(J_8, w) → K_{22}
  464. Translate(R_7, w) → L_{22}
  465. PolyLine(P_{21}, Q_{21}, B_{22}, C_{22}, D_{22}, E_{22}, F_{22}, G_{22}, H_{22}, I_{22}, J_{22}, K_{22}, R_{21}, L_{22}, S_{21}, T_{21}, U_{21}, V_{21}, W_{21}, Z_{21}, A_{22}) → sterbi'_5
  466. Translate(Q_7, w) → M_{22}
  467. Translate(R_7, w) → N_{22}
  468. Translate(H_7, w) → O_{22}
  469. Translate(S_7, w) → P_{22}
  470. Translate(J_7, w) → Q_{22}
  471. Translate(T_7, w) → R_{22}
  472. Translate(K_7, w) → S_{22}
  473. Translate(U_7, w) → T_{22}
  474. Translate(L_7, w) → U_{22}
  475. Translate(V_7, w) → V_{22}
  476. Translate(I_7, w) → W_{22}
  477. Translate(W_7, w) → Z_{22}
  478. Translate(M_7, w) → A_{23}
  479. Translate(Z_7, w) → B_{23}
  480. Translate(N_7, w) → C_{23}
  481. Translate(A_8, w) → D_{23}
  482. Translate(O_7, w) → E_{23}
  483. Translate(B_8, w) → F_{23}
  484. Translate(P_7, w) → G_{23}
  485. Translate(C_8, w) → H_{23}
  486. Translate(Q_7, w) → I_{23}
  487. PolyLine(M_{22}, N_{22}, W_{22}, Z_{22}, A_{23}, B_{23}, C_{23}, D_{23}, E_{23}, F_{23}, G_{23}, H_{23}, O_{22}, I_{23}, P_{22}, Q_{22}, R_{22}, S_{22}, T_{22}, U_{22}, V_{22}) → sterbu'_5
  488. Translate(roosrij, w) → roosrij'_5
  489. Translate(R_7, Vector[(2 * v)]) → J_{23}
  490. Translate(D_8, Vector[(2 * v)]) → K_{23}
  491. Translate(S_7, Vector[(2 * v)]) → L_{23}
  492. Translate(M_8, Vector[(2 * v)]) → M_{23}
  493. Translate(T_7, Vector[(2 * v)]) → N_{23}
  494. Translate(E_8, Vector[(2 * v)]) → O_{23}
  495. Translate(U_7, Vector[(2 * v)]) → P_{23}
  496. Translate(F_8, Vector[(2 * v)]) → Q_{23}
  497. Translate(V_7, Vector[(2 * v)]) → R_{23}
  498. Translate(G_8, Vector[(2 * v)]) → S_{23}
  499. Translate(W_7, Vector[(2 * v)]) → T_{23}
  500. Translate(I_8, Vector[(2 * v)]) → U_{23}
  501. Translate(Z_7, Vector[(2 * v)]) → V_{23}
  502. Translate(H_8, Vector[(2 * v)]) → W_{23}
  503. Translate(A_8, Vector[(2 * v)]) → Z_{23}
  504. Translate(K_8, Vector[(2 * v)]) → A_{24}
  505. Translate(B_8, Vector[(2 * v)]) → B_{24}
  506. Translate(L_8, Vector[(2 * v)]) → C_{24}
  507. Translate(C_8, Vector[(2 * v)]) → D_{24}
  508. Translate(J_8, Vector[(2 * v)]) → E_{24}
  509. Translate(R_7, Vector[(2 * v)]) → F_{24}
  510. PolyLine(J_{23}, K_{23}, T_{23}, U_{23}, V_{23}, W_{23}, Z_{23}, A_{24}, B_{24}, C_{24}, D_{24}, E_{24}, L_{23}, F_{24}, M_{23}, N_{23}, O_{23}, P_{23}, Q_{23}, R_{23}, S_{23}) → sterbi'_6
  511. Translate(Q_7, Vector[(2 * v)]) → G_{24}
  512. Translate(R_7, Vector[(2 * v)]) → H_{24}
  513. Translate(H_7, Vector[(2 * v)]) → I_{24}
  514. Translate(S_7, Vector[(2 * v)]) → J_{24}
  515. Translate(J_7, Vector[(2 * v)]) → K_{24}
  516. Translate(T_7, Vector[(2 * v)]) → L_{24}
  517. Translate(K_7, Vector[(2 * v)]) → M_{24}
  518. Translate(U_7, Vector[(2 * v)]) → N_{24}
  519. Translate(L_7, Vector[(2 * v)]) → O_{24}
  520. Translate(V_7, Vector[(2 * v)]) → P_{24}
  521. Translate(I_7, Vector[(2 * v)]) → Q_{24}
  522. Translate(W_7, Vector[(2 * v)]) → R_{24}
  523. Translate(M_7, Vector[(2 * v)]) → S_{24}
  524. Translate(Z_7, Vector[(2 * v)]) → T_{24}
  525. Translate(N_7, Vector[(2 * v)]) → U_{24}
  526. Translate(A_8, Vector[(2 * v)]) → V_{24}
  527. Translate(O_7, Vector[(2 * v)]) → W_{24}
  528. Translate(B_8, Vector[(2 * v)]) → Z_{24}
  529. Translate(P_7, Vector[(2 * v)]) → A_{25}
  530. Translate(C_8, Vector[(2 * v)]) → B_{25}
  531. Translate(Q_7, Vector[(2 * v)]) → C_{25}
  532. PolyLine(G_{24}, H_{24}, Q_{24}, R_{24}, S_{24}, T_{24}, U_{24}, V_{24}, W_{24}, Z_{24}, A_{25}, B_{25}, I_{24}, C_{25}, J_{24}, K_{24}, L_{24}, M_{24}, N_{24}, O_{24}, P_{24}) → sterbu'_6
  533. Translate(roosrij, Vector[(2 * v)]) → roosrij'_6

AI Drawing Prompt Reference

Create an Islamic geometric pattern based on decagons and pentagons. Start with a regular decagon, rotate it by 36 degrees to form a second decagon sharing edges. On each side of the decagons, construct regular pentagons pointing outward or inward, creating star-like and petal shapes. Connect vertices of these pentagons to generate additional decagons and pentagons, layering them to form a periodic tiling with rich rotational and mirror symmetry. The final design is a complex interlocking grid of polygons with clear lines.
The prompt above was compiled from the original drawing commands and is for reference only.