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Pythagorean Tessellation #122 Tiling

Pythagorean Tessellation #122 Tiling
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2015-01-11 04:09
TrianglePolygonTransformationGeometric Construction
This example demonstrates geometric tiling based on the Pythagorean theorem, creating a continuous pattern through the combination of different triangles. Core math concepts include the Pythagorean theorem, polygon construction, rotational symmetry, and the application of rational numbers in geometry. Construction highlights involve using GeoGebra commands like Line, OrthogonalLine, Point, Segment, Intersect, and Polygon, along with objects A, B, a, b, c, C, d, D, e, E, f, F, g, G, h, H, i, I, j, J, k, K, l, L, M, m, N, O, p, P, Q, R, r, S, T, t, U, a_1, V, W. Suitable for high school mathematics education, exploring geometric transformations, spatial tiling, and the practical application of theorems.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. OrthogonalLine(B, a) → b
  3. OrthogonalLine(A, a) → c
  4. Point(c) → C
  5. OrthogonalLine(C, c) → d
  6. Point(b) → D
  7. OrthogonalLine(D, b) → e
  8. Point(b) → E
  9. OrthogonalLine(E, b) → f
  10. Point(b) → F
  11. OrthogonalLine(F, b) → g
  12. Point(b) → G
  13. OrthogonalLine(G, b) → h
  14. Point(d) → H
  15. OrthogonalLine(H, d) → i
  16. Point(d) → I
  17. OrthogonalLine(I, d) → j
  18. Point(j) → J
  19. OrthogonalLine(J, j) → k
  20. Point(k) → K
  21. OrthogonalLine(K, k) → l
  22. Point(c) → M
  23. Segment(L, M) → m
  24. Point(a) → O
  25. Segment(N, O) → p
  26. Intersect(b, k) → P
  27. Point(b) → R
  28. Segment(Q, R) → r
  29. Intersect(c, k) → S
  30. Segment(A, T) → t
  31. Point(k) → U
  32. Segment(T, U) → a_1
  33. Point(b) → V
  34. Segment(V, W) → b_1
  35. Segment(W, A) → c_1
  36. Segment(Z, O) → e_1
  37. Intersect(b, d) → A_1
  38. Point(c) → C_1
  39. Segment(B_1, C_1) → g_1
  40. Point(d) → E_1
  41. Segment(D_1, E_1) → i_1
  42. Segment(A, F_1) → j_1
  43. Point(i) → G_1
  44. Segment(F_1, G_1) → k_1
  45. Segment(S, H_1) → l_1
  46. Point(a) → I_1
  47. Segment(H_1, I_1) → m_1
  48. Intersect(a, i) → J_1
  49. Segment(J_1, K_1) → n_1
  50. Point(k) → L_1
  51. Segment(K_1, L_1) → p_1
  52. Intersect(i, k) → M_1
  53. Segment(M_1, N_1) → q_1
  54. Segment(N_1, M) → r_1
  55. Point(d) → R_1
  56. Point(i) → T_1
  57. Intersect(p, r) → U_1
  58. Intersect(r, a_1) → V_1
  59. Intersect(m, a_1) → W_1
  60. Intersect(m, p) → Z_1
  61. Polygon(U_1, V_1, W_1, Z_1) → poly1, u_1, v_1, w_1, z_1
  62. Intersect(k_1, m_1) → E_2
  63. Intersect(m_1, r_1) → F_2
  64. Intersect(p_1, r_1) → G_2
  65. Intersect(k_1, p_1) → H_2
  66. Polygon(E_2, F_2, G_2, H_2) → poly3, e_3, f_3, g_2, h_2
  67. Segment(M, G_2) → p_2
  68. Segment(H_2, L_1) → q_2
  69. Segment(E_2, G_1) → r_2
  70. Segment(M_2, C) → t_2
  71. Intersect(c, e) → N_2
  72. Segment(N_2, O_2) → g_3
  73. Segment(O_2, E_1) → h_3
  74. Point(b) → P_2
  75. Segment(M_2, P_2) → i_3
  76. Segment(Q_2, A_1) → j_3
  77. Segment(D, R_2) → k_3
  78. Segment(R_2, S_2) → l_3
  79. Segment(S_2, H) → m_3
  80. Segment(T_2, C) → n_3
  81. Intersect(c, f) → U_2
  82. Segment(U_2, V_2) → p_3
  83. Segment(V_2, Q_2) → q_3
  84. Segment(W_2, D) → r_3
  85. Intersect(c, g) → Z_2
  86. Segment(Z_2, A_3) → s_3
  87. Segment(A_3, W_2) → t_3
  88. Segment(B_3, E) → a_4
  89. Intersect(e, i) → D_3
  90. Segment(C_3, D_3) → b_4
  91. Segment(C_3, B_3) → c_4
  92. Point(b) → E_3
  93. Segment(E_3, F_3) → d_4
  94. Segment(F_3, N_2) → e_4
  95. Segment(G_3, N_2) → f_4
  96. Segment(N_2, H_3) → g_4
  97. Segment(I_3, E) → h_4
  98. Intersect(c, h) → J_3
  99. Segment(J_3, K_3) → i_4
  100. Segment(K_3, I_3) → j_4
  101. Segment(L_3, M_3) → k_4
  102. Point(b) → N_3
  103. Segment(L_3, N_3) → l_4
  104. Segment(F, O_3) → m_4
  105. Segment(O_3, P_3) → n_4
  106. Intersect(f, i) → Q_3
  107. Segment(P_3, Q_3) → p_4
  108. Segment(R_3, M_3) → q_4
  109. Intersect(h, i) → S_3
  110. Segment(S_3, T_3) → r_4
  111. Segment(T_3, R_3) → s_4
  112. Intersect(g, i) → U_3
  113. Segment(U_3, V_3) → t_4
  114. Segment(V_3, G_3) → a_5
  115. Segment(Q_3, W_3) → b_5
  116. Segment(T_2, W_3) → c_5
  117. Point(i) → Z_3
  118. Segment(Z_3, H_3) → d_5
  119. Segment(D_3, A_4) → e_5
  120. Segment(A_4, R_1) → f_5
  121. Segment(B_4, Z_2) → g_5
  122. Point(h) → C_4
  123. Segment(B_4, C_4) → h_5
  124. Segment(J_3, D_4) → i_5
  125. Intersect(g, j) → F_4
  126. Segment(E_4, F_4) → j_5
  127. Segment(E_4, D_4) → k_5
  128. Segment(G_4, H_4) → l_5
  129. Point(b) → I_4
  130. Segment(H_4, I_4) → m_5
  131. Point(i) → J_4
  132. Segment(J_4, G_4) → n_5
  133. Segment(K_4, M_3) → p_5
  134. Segment(F, L_4) → q_5
  135. Point(h) → M_4
  136. Segment(L_4, M_4) → r_5
  137. Segment(G, N_4) → s_5
  138. Segment(N_4, O_4) → t_5
  139. Segment(O_4, U_3) → a_6
  140. Segment(M_1, P_4) → b_6
  141. Segment(J_1, R_4) → c_6
  142. Point(j) → S_4
  143. Segment(R_4, S_4) → d_6
  144. Point(a) → T_4
  145. Segment(P_4, T_4) → e_6
  146. Intersect(a, j) → U_4
  147. Segment(U_4, V_4) → f_6
  148. Point(k) → W_4
  149. Segment(V_4, W_4) → g_6
  150. Segment(J, Z_4) → h_6
  151. Segment(Z_4, G_1) → i_6
  152. Segment(Q_4, U_4) → j_6
  153. Segment(U_4, A_5) → k_6
  154. Segment(Q_4, T_1) → l_6
  155. Segment(B_5, J_1) → m_6
  156. Intersect(e, j) → C_5
  157. Segment(C_5, D_5) → n_6
  158. Segment(D_5, B_5) → p_6
  159. Segment(E_5, H) → q_6
  160. Point(j) → F_5
  161. Segment(F_5, E_5) → r_6
  162. Segment(I, G_5) → s_6
  163. Segment(G_5, T_4) → t_6
  164. Segment(I, H_5) → a_7
  165. Segment(H_5, Z_3) → b_7
  166. Segment(I_5, H) → c_7
  167. Point(e) → J_5
  168. Segment(J_5, I_5) → d_7
  169. Segment(D_3, K_5) → e_7
  170. Point(j) → L_5
  171. Segment(K_5, L_5) → f_7
  172. Segment(M_5, D_3) → g_7
  173. Segment(F_4, N_5) → h_7
  174. Segment(N_5, M_5) → i_7
  175. Segment(O_5, C_5) → j_7
  176. Point(i) → P_5
  177. Segment(P_5, O_5) → k_7
  178. Segment(P_5, K_4) → l_7
  179. Segment(Q_5, C_5) → m_7
  180. Segment(C_5, R_5) → n_7
  181. Intersect(f, j) → T_5
  182. Segment(S_5, T_5) → p_7
  183. Intersect(l_3, q_3) → U_5
  184. Intersect(i_3, q_3) → V_5
  185. Intersect(h_3, i_3) → W_5
  186. Intersect(h_3, l_3) → Z_5
  187. Polygon(U_5, V_5, W_5, Z_5) → poly5, u_5, v_5, w_5, z_5
  188. Intersect(t_3, c_4) → A_6
  189. Intersect(t_3, d_4) → B_6
  190. Intersect(q_3, d_4) → C_6
  191. Intersect(q_3, c_4) → D_6
  192. Polygon(A_6, B_6, C_6, D_6) → poly6, a_8, b_8, c_8, d_8
  193. Intersect(j_4, n_4) → E_6
  194. Intersect(j_4, l_4) → F_6
  195. Intersect(t_3, l_4) → G_6
  196. Intersect(t_3, n_4) → H_6
  197. Polygon(E_6, F_6, G_6, H_6) → poly7, e_8, f_8, g_8, h_8
  198. Intersect(r_5, t_5) → I_6
  199. Intersect(m_5, r_5) → J_6
  200. Intersect(j_4, m_5) → K_6
  201. Intersect(j_4, t_5) → L_6
  202. Polygon(I_6, J_6, K_6, L_6) → poly8, i_8, j_8, k_8, l_8
  203. Intersect(h_5, k_5) → M_6
  204. Intersect(h_5, t_5) → N_6
  205. Intersect(s_4, t_5) → O_6
  206. Intersect(s_4, k_5) → P_6
  207. Polygon(M_6, N_6, O_6, P_6) → poly9, m_8, n_8, o_6, p_8
  208. Intersect(a_5, n_5) → Q_6
  209. Intersect(s_4, n_5) → R_6
  210. Intersect(n_4, s_4) → S_6
  211. Intersect(n_4, a_5) → T_6
  212. Polygon(Q_6, R_6, S_6, T_6) → poly10, q_7, r_7, s_7, t_7
  213. Intersect(c_5, l_7) → U_6
  214. Intersect(a_5, l_7) → V_6
  215. Intersect(c_4, a_5) → W_6
  216. Intersect(c_4, c_5) → Z_6
  217. Polygon(U_6, V_6, W_6, Z_6) → poly11, u_6, v_6, w_6, z_6
  218. Intersect(c_5, d_5) → A_7
  219. Intersect(l_3, c_5) → B_7
  220. Intersect(l_3, f_5) → C_7
  221. Intersect(d_5, f_5) → D_7
  222. Polygon(A_7, B_7, C_7, D_7) → poly12, a_9, b_9, c_9, d_9
  223. Segment(K, E_7) → q_8
  224. Segment(E_7, S_4) → r_8
  225. Segment(F_7, J) → s_8
  226. Intersect(d, l) → G_7
  227. Segment(G_7, H_7) → t_8
  228. Segment(H_7, F_7) → e_9
  229. Intersect(a, l) → K_7
  230. Segment(K_7, J_7) → g_9
  231. Segment(I, I_7) → f_9
  232. Point(l) → L_7
  233. Segment(I_7, L_7) → h_9
  234. Point(k) → M_7
  235. Segment(J_7, M_7) → i_9
  236. Segment(N_7, U_4) → j_9
  237. Point(l) → O_7
  238. Segment(O_7, N_7) → k_9
  239. Segment(K_7, P_7) → l_9
  240. Segment(P_7, F_5) → m_9
  241. Intersect(e, l) → Q_7
  242. Segment(Q_7, R_7) → n_9
  243. Segment(R_7, A_5) → p_9
  244. Segment(I, S_7) → q_9
  245. Intersect(f, l) → T_7
  246. Segment(T_7, U_7) → r_9
  247. Segment(U_7, S_7) → s_9
  248. Point(l) → V_7
  249. Segment(V_7, R_5) → t_9
  250. Segment(L_5, W_7) → a_{10}
  251. Segment(W_7, G_7) → b_{10}
  252. Point(l) → Z_7
  253. Segment(Z_7, S_5) → c_{10}
  254. Point(f) → A_8
  255. Segment(A_8, Q_5) → d_{10}
  256. Segment(T_5, B_8) → e_{10}
  257. Segment(B_8, J_5) → f_{10}
  258. Segment(C_8, Q_3) → g_{10}
  259. Segment(Q_3, D_8) → h_{10}
  260. Segment(D_8, E_8) → i_{10}
  261. Segment(E_8, Q_7) → j_{10}
  262. Intersect(h, j) → F_8
  263. Segment(F_8, G_8) → k_{10}
  264. Segment(G_8, C_8) → l_{10}
  265. Segment(T_7, H_8) → m_{10}
  266. Segment(H_8, J_4) → n_{10}
  267. Segment(U_3, I_8) → p_{10}
  268. Point(l) → J_8
  269. Segment(I_8, J_8) → q_{10}
  270. Segment(K_8, T_5) → r_{10}
  271. Segment(L_8, T_5) → s_{10}
  272. Segment(L_8, J_4) → t_{10}
  273. Segment(H_8, I_8) → a_{11}
  274. Intersect(h, l) → M_8
  275. Segment(M_8, N_8) → b_{11}
  276. Segment(N_8, K_8) → c_{11}
  277. Intersect(g, l) → O_8
  278. Segment(O_8, P_8) → d_{11}
  279. Segment(P_8, A_8) → e_{11}
  280. Segment(Q_8, F_4) → f_{11}
  281. Segment(J_8, Q_8) → g_{11}
  282. Segment(O_8, R_8) → h_{11}
  283. Segment(R_8, S_8) → i_{11}
  284. Segment(S_8, S_3) → j_{11}
  285. Segment(F_8, T_8) → k_{11}
  286. Point(l) → U_8
  287. Segment(T_8, U_8) → l_{11}
  288. Segment(V_8, F_4) → m_{11}
  289. Point(h) → W_8
  290. Segment(V_8, W_8) → n_{11}
  291. Intersect(d_6, e_6) → Z_8
  292. Intersect(e_6, i_6) → A_9
  293. Intersect(g_6, i_6) → B_9
  294. Intersect(d_6, g_6) → C_9
  295. Polygon(Z_8, A_9, B_9, C_9) → poly13, z_8, a_{12}, b_{12}, c_{12}
  296. Intersect(p_6, r_6) → D_9
  297. Intersect(l_6, p_6) → E_9
  298. Intersect(l_6, t_6) → F_9
  299. Intersect(r_6, t_6) → G_9
  300. Polygon(D_9, E_9, F_9, G_9) → poly14, d_{12}, e_{12}, f_{12}, g_{12}
  301. Intersect(d_7, f_7) → H_9
  302. Intersect(b_7, d_7) → I_9
  303. Intersect(p_6, b_7) → J_9
  304. Intersect(p_6, f_7) → K_9
  305. Polygon(H_9, I_9, J_9, K_9) → poly15, h_{12}, i_{12}, j_{12}, k_{12}
  306. Intersect(i_7, i_{10}) → L_9
  307. Intersect(i_7, k_7) → M_9
  308. Intersect(k_7, f_{10}) → N_9
  309. Intersect(f_{10}, i_{10}) → O_9
  310. Polygon(L_9, M_9, N_9, O_9) → poly16, l_{12}, m_{12}, n_{12}, o_9
  311. Intersect(l_{10}, a_{11}) → P_9
  312. Intersect(l_{10}, t_{10}) → Q_9
  313. Intersect(i_7, t_{10}) → R_9
  314. Intersect(i_7, a_{11}) → S_9
  315. Polygon(P_9, Q_9, R_9, S_9) → poly17, p_{11}, q_{11}, r_{11}, s_{11}
  316. Segment(T_9, U_3) → t_{11}
  317. Point(h) → U_9
  318. Segment(T_9, U_9) → p_{12}
  319. Intersect(i_{11}, p_{12}) → V_9
  320. Intersect(k_5, p_{12}) → W_9
  321. Intersect(k_5, l_{10}) → Z_9
  322. Intersect(l_{10}, i_{11}) → A_{10}
  323. Polygon(V_9, W_9, Z_9, A_{10}) → poly18, v_9, w_9, z_9, a_{13}
  324. Intersect(l_{11}, n_{11}) → B_{10}
  325. Intersect(i_{11}, n_{11}) → C_{10}
  326. Intersect(c_{11}, i_{11}) → D_{10}
  327. Intersect(c_{11}, l_{11}) → E_{10}
  328. Polygon(B_{10}, C_{10}, D_{10}, E_{10}) → poly19, b_{13}, c_{13}, d_{13}, e_{13}
  329. Intersect(c_{11}, g_{11}) → F_{10}
  330. Intersect(a_{11}, c_{11}) → G_{10}
  331. Intersect(a_{11}, e_{11}) → H_{10}
  332. Intersect(e_{11}, g_{11}) → I_{10}
  333. Polygon(F_{10}, G_{10}, H_{10}, I_{10}) → poly20, f_{13}, g_{13}, h_{13}, i_{13}
  334. Intersect(c_{10}, d_{10}) → J_{10}
  335. Intersect(d_{10}, i_{10}) → K_{10}
  336. Intersect(s_9, i_{10}) → L_{10}
  337. Intersect(s_9, c_{10}) → M_{10}
  338. Polygon(J_{10}, K_{10}, L_{10}, M_{10}) → poly21, j_{13}, k_{13}, l_{13}, m_{13}
  339. Intersect(s_9, t_9) → N_{10}
  340. Intersect(s_9, a_{10}) → O_{10}
  341. Intersect(p_9, a_{10}) → P_{10}
  342. Intersect(p_9, t_9) → Q_{10}
  343. Polygon(N_{10}, O_{10}, P_{10}, Q_{10}) → poly22, n_{13}, o_{10}, p_{13}, q_{12}
  344. Intersect(h_9, p_9) → R_{10}
  345. Intersect(m_9, p_9) → S_{10}
  346. Intersect(e_9, m_9) → T_{10}
  347. Intersect(e_9, h_9) → U_{10}
  348. Polygon(R_{10}, S_{10}, T_{10}, U_{10}) → poly23, r_{12}, s_{12}, t_{12}, u_{10}
  349. Intersect(e_9, k_9) → V_{10}
  350. Intersect(r_8, e_9) → W_{10}
  351. Intersect(r_8, i_9) → Z_{10}
  352. Intersect(i_9, k_9) → A_{11}
  353. Polygon(V_{10}, W_{10}, Z_{10}, A_{11}) → poly24, v_{10}, w_{10}, z_{10}, a_{14}
  354. Segment(P, B_{11}) → q
  355. Segment(B_{11}, O) → s
  356. Segment(A, C_{11}) → m_2
  357. Segment(C_{11}, U) → n_2
  358. Segment(D_{11}, S) → q_{13}
  359. Segment(D_{11}, R) → r_{13}
  360. Segment(B, E_{11}) → s_{13}
  361. Segment(E_{11}, M) → t_{13}
  362. Intersect(s, t_{13}) → F_{11}
  363. Intersect(s, r_{13}) → G_{11}
  364. Intersect(n_2, r_{13}) → H_{11}
  365. Intersect(n_2, t_{13}) → I_{11}
  366. Polygon(F_{11}, G_{11}, H_{11}, I_{11}) → poly25, f_{14}, g_{14}, h_{14}, i_{14}
  367. Segment(J_1, O_1) → n
  368. Segment(O_1, P_1) → d_1
  369. Segment(P_1, A_1) → f_1
  370. Segment(B, Q_1) → h_1
  371. Segment(Q_1, E_1) → s_1
  372. Segment(C, S_1) → t_1
  373. Segment(S_1, O) → a_2
  374. Segment(A_2, A) → b_2
  375. Segment(R_1, A_2) → c_2
  376. Segment(C, B_2) → d_2
  377. Segment(B_2, T_1) → e_2
  378. Segment(H, C_2) → f_2
  379. Segment(C_2, I_1) → i_2
  380. Intersect(c_2, e_2) → D_2
  381. Intersect(d_1, c_2) → I_2
  382. Intersect(d_1, i_2) → J_2
  383. Intersect(e_2, i_2) → K_2
  384. Polygon(D_2, I_2, J_2, K_2) → poly2, d_3, i_{15}, j_2, k_2
  385. Segment(A, L_2) → l_2
  386. Segment(L_2, V) → s_2
  387. Intersect(d_1, s_1) → J_{11}
  388. Intersect(s_1, s_2) → K_{11}
  389. Intersect(a_2, s_2) → L_{11}
  390. Intersect(d_1, a_2) → M_{11}
  391. Polygon(J_{11}, K_{11}, L_{11}, M_{11}) → poly4, j_{14}, k_{14}, l_{14}, m_{14}
  392. Segment(B_{11}, R) → a_3
  393. Segment(E_{11}, O) → b_3
  394. Segment(M, C_{11}) → c_3
  395. Segment(D_{11}, U) → b_{14}
  396. Segment(Q_1, V) → c_{14}
  397. Segment(P_1, E_1) → d_{14}
  398. Segment(S_1, C_1) → e_{14}
  399. Segment(L_2, O) → n_{14}
  400. Segment(Q_2, P_2) → p_{14}
  401. Intersect(e, q_3) → N_{11}
  402. Segment(R_2, N_{11}) → q_{14}
  403. Intersect(c, l_3) → O_{11}
  404. Segment(O_2, O_{11}) → r_{14}
  405. Segment(M_2, E_1) → s_{14}
  406. Segment(W_2, E_3) → t_{14}
  407. Intersect(f, t_3) → P_{11}
  408. Segment(B_3, P_{11}) → a_{15}
  409. Intersect(c, c_4) → Q_{11}
  410. Segment(V_2, Q_{11}) → b_{15}
  411. Segment(F_3, N_{11}) → c_{15}
  412. Segment(L_3, P_{11}) → d_{15}
  413. Segment(I_3, N_3) → e_{15}
  414. Intersect(g, j_4) → R_{11}
  415. Segment(O_3, R_{11}) → f_{15}
  416. Intersect(c, n_4) → S_{11}
  417. Segment(A_3, S_{11}) → g_{15}
  418. Segment(L_4, I_4) → h_{15}
  419. Segment(N_4, M_4) → j_{15}
  420. Intersect(c, t_5) → T_{11}
  421. Segment(K_3, T_{11}) → k_{15}
  422. Segment(H_4, R_{11}) → l_{15}
  423. Segment(B_4, T_{11}) → m_{15}
  424. Segment(D_4, C_4) → n_{15}
  425. Intersect(i, k_5) → U_{11}
  426. Segment(T_3, U_{11}) → p_{15}
  427. Intersect(g, s_4) → V_{11}
  428. Segment(O_4, V_{11}) → q_{15}
  429. Segment(M, H_1) → r_{15}
  430. Segment(F_1, I_1) → s_{15}
  431. Segment(I_1, O_1) → t_{15}
  432. Segment(K_1, G_1) → a_{16}
  433. Segment(G_1, P_4) → b_{16}
  434. Segment(N_1, L_1) → c_{16}
  435. Segment(R_1, B_2) → d_{16}
  436. Segment(S_2, R_1) → e_{16}
  437. Segment(T_2, O_{11}) → f_{16}
  438. Intersect(e, c_5) → W_{11}
  439. Segment(C_3, W_{11}) → g_{16}
  440. Segment(W_{11}, H_3) → h_{16}
  441. Segment(G_3, Q_{11}) → i_{16}
  442. Segment(C_2, T_1) → j_{16}
  443. Segment(T_1, B_5) → k_{16}
  444. Segment(I_5, Z_3) → l_{16}
  445. Segment(Z_3, A_4) → m_{16}
  446. Segment(A_2, C_1) → n_{16}
  447. Intersect(f, a_5) → Z_{11}
  448. Segment(P_3, Z_{11}) → p_{16}
  449. Segment(Z_{11}, K_4) → q_{16}
  450. Segment(R_3, S_{11}) → r_{16}
  451. Segment(V_{11}, G_4) → s_{16}
  452. Segment(V_3, J_4) → t_{16}
  453. Segment(J_4, C_8) → a_{17}
  454. Intersect(f, i_7) → A_{12}
  455. Segment(A_{12}, D_8) → b_{17}
  456. Segment(P_5, M_5) → c_{17}
  457. Segment(P_5, W_3) → d_{17}
  458. Segment(K_5, J_5) → e_{17}
  459. Segment(J_5, O_5) → f_{17}
  460. Intersect(g, l_{10}) → B_{12}
  461. Segment(E_4, B_{12}) → g_{17}
  462. Segment(B_{12}, I_8) → h_{17}
  463. Segment(T_9, U_{11}) → i_{17}
  464. Segment(S_8, U_9) → j_{17}
  465. Intersect(j, i_{11}) → C_{12}
  466. Segment(G_8, C_{12}) → k_{17}
  467. Segment(V_8, C_{12}) → l_{17}
  468. Segment(W_4, Z_4) → m_{17}
  469. Segment(F_7, S_4) → n_{17}
  470. Segment(S_4, V_4) → p_{17}
  471. Segment(Q_4, T_4) → q_{17}
  472. Segment(T_4, R_4) → r_{17}
  473. Intersect(a, e_9) → E_{12}
  474. Segment(E_{12}, N_7) → s_{17}
  475. Segment(P_7, E_{12}) → t_{17}
  476. Segment(E_7, M_7) → a_{18}
  477. Segment(O_7, J_7) → b_{18}
  478. Segment(A_5, F_5) → c_{18}
  479. Intersect(d, p_9) → F_{12}
  480. Segment(I_7, F_{12}) → d_{18}
  481. Segment(W_7, F_{12}) → e_{18}
  482. Segment(S_7, L_5) → f_{18}
  483. Segment(L_5, D_5) → g_{18}
  484. Intersect(d, p_6) → G_{12}
  485. Segment(E_5, G_{12}) → h_{18}
  486. Segment(G_{12}, H_5) → i_{18}
  487. Segment(G_5, F_5) → j_{18}
  488. Intersect(e, s_9) → H_{12}
  489. Segment(E_8, H_{12}) → k_{18}
  490. Segment(H_{12}, R_5) → l_{18}
  491. Segment(R_7, V_7) → m_{18}
  492. Intersect(j, i_{10}) → I_{12}
  493. Segment(Q_5, I_{12}) → n_{18}
  494. Segment(I_{12}, B_8) → p_{18}
  495. Segment(L_8, A_{12}) → q_{18}
  496. Segment(S_5, A_8) → r_{18}
  497. Segment(A_8, H_8) → s_{18}
  498. Intersect(g, c_{11}) → J_{12}
  499. Segment(Q_8, J_{12}) → t_{18}
  500. Segment(J_{12}, R_8) → a_{19}
  501. Segment(T_8, W_8) → b_{19}
  502. Segment(N_8, U_8) → c_{19}
  503. Segment(J_8, P_8) → d_{19}
  504. Intersect(j, a_{11}) → K_{12}
  505. Segment(K_8, K_{12}) → e_{19}
  506. Segment(K_{12}, N_5) → f_{19}
  507. Segment(U_7, Z_7) → g_{19}
  508. Segment(H_7, L_7) → h_{19}
  509. Polygon(N_7, V_{10}, E_{12}, T_{10}, P_7) → poly26, n_{19}, v_2, e_{20}, t_{19}, p_{19}
  510. Polygon(V_4, C_9, W_{10}, F_7, S_4) → poly27, v_4, c_{20}, w_2, f_{20}, s_{19}
  511. Polygon(A_5, G_5, G_9, F_5, S_{10}) → poly28, a_{20}, g_{20}, g_{21}, f_{21}, s_{20}
  512. Polygon(R_4, Z_8, T_4, F_9, Q_4) → poly29, r_{19}, z_2, t_{20}, f_{22}, q_{19}
  513. Polygon(E_5, D_9, G_{12}, J_9, H_5) → poly30, e_{21}, d_{20}, g_{22}, j_{19}, h_{20}
  514. Polygon(K_2, C_2, T_1, B_5, E_9) → poly31, k_{19}, c_{21}, t_{21}, b_{20}, e_{22}
  515. Polygon(D_7, A_4, Z_3, I_5, I_9) → poly32, d_{21}, a_{21}, z_3, i_{19}, i_{20}
  516. Polygon(Z_{10}, M_7, E_7) → poly33, e_{23}, z_4, m_{19}
  517. Polygon(A_{11}, O_7, J_7) → poly34, j_{20}, a_{22}, o_7
  518. Polygon(H_7, U_{10}, L_7) → poly35, l_{19}, h_{21}, u_2
  519. Polygon(I_7, R_{10}, P_{10}, W_7, F_{12}) → poly36, i_{21}, r_{20}, p_{20}, w_7, f_{23}
  520. Polygon(S_7, D_5, K_9, L_5, O_{10}) → poly37, s_{21}, d_{22}, k_{20}, l_{20}, o_1
  521. Polygon(R_7, Q_{10}, V_7) → poly38, v_7, r_{21}, q_{20}
  522. Polygon(W_4, Z_4, B_9) → poly39, b_{21}, w_4, z_7
  523. Polygon(P_4, K_1, H_2, G_1, A_9) → poly40, p_{21}, k_{21}, h_{22}, g_{23}, a_{23}
  524. Polygon(G_2, L_1, N_1) → poly41, n_{20}, g_{24}, l_{21}
  525. Polygon(F_1, E_2, J_2, O_1, I_1) → poly42, f_{24}, e_{24}, j_{21}, o_2, i_{22}
  526. Polygon(H_1, C_{11}, I_{11}, M, F_2) → poly43, h_{23}, c_{22}, i_{23}, m_{20}, f_{25}
  527. Polygon(U, D_{11}, H_{11}) → poly44, h_{24}, u, d_{23}
  528. Polygon(B_{11}, R, G_{11}) → poly45, g_{25}, b_{22}, r_{22}
  529. Polygon(F_{11}, E_{11}, L_2, L_{11}, O) → poly46, f_{26}, e_{25}, l_{22}, l_{23}, o
  530. Polygon(Q_1, V, K_{11}) → poly47, k_{22}, q_{21}, v
  531. Polygon(J_{11}, W_5, M_2, E_1, P_1) → poly48, j_{22}, w_3, m_{21}, e_{26}, p_{22}
  532. Polygon(M_{11}, I_2, A_2, C_1, S_1) → poly49, m_{22}, i_{24}, a_{24}, c_{23}, s_{22}
  533. Polygon(Q_2, P_2, V_5) → poly50, v_3, q_{22}, p_{23}
  534. Polygon(U_5, R_2, N_{11}, F_3, C_6) → poly51, u_3, r_{23}, n_{21}, f_{27}, c_{24}
  535. Polygon(O_2, T_2, B_7, O_{11}, Z_5) → poly52, o_3, t_{22}, b_{23}, o_{11}, z_{11}
  536. Polygon(W_2, B_6, E_3) → poly53, e_{27}, w_8, b_{24}
  537. Polygon(S_2, B_2, D_2, R_1, C_7) → poly54, s_{23}, b_{25}, d_{24}, r_{24}, c_{25}
  538. Polygon(W_6, D_6, V_2, Q_{11}, G_3) → poly55, w_{11}, d_{25}, v_8, q_{23}, g_{26}
  539. Polygon(H_3, A_7, W_{11}, Z_6, C_3) → poly56, h_{25}, a_{25}, w_{12}, z_{12}, c_{26}
  540. Polygon(L_3, G_6, P_{11}, A_6, B_3) → poly57, l_{24}, g_{27}, p_{24}, a_{26}, b_{26}
  541. Polygon(N_3, I_3, F_6) → poly58, f_{28}, n_{22}, i_{25}
  542. Polygon(E_6, K_6, H_4, R_{11}, O_3) → poly59, e_{28}, k_{23}, h_{26}, r_{25}, o_4
  543. Polygon(H_6, S_6, R_3, S_{11}, A_3) → poly60, h_{27}, s_{24}, r_{26}, s_{25}, a_{27}
  544. Polygon(L_4, J_6, I_4) → poly61, i_{26}, l_{25}, j_{23}
  545. Polygon(N_4, I_6, M_4) → poly62, m_{23}, n_{23}, i_{27}
  546. Polygon(K_4, V_6, Z_{11}, T_6, P_3) → poly63, k_{24}, v_{11}, z_{13}, t_{23}, p_{25}
  547. Polygon(R_6, G_4, V_{11}, O_4, O_6) → poly64, r_{27}, g_{28}, v_{12}, o_5, o_8
  548. Polygon(B_4, T_{11}, K_3, L_6, N_6) → poly65, b_{27}, t_{24}, k_{25}, l_{26}, n_{24}
  549. Polygon(M_6, D_4, C_4) → poly66, c_{27}, m_{24}, d_{26}
  550. Polygon(C_8, J_4, V_3, Q_6, Q_9) → poly67, c_{28}, j_{24}, v_{13}, q_{24}, q_{25}
  551. Polygon(M_9, U_6, W_3, P_5, M_5) → poly68, m_{25}, u_4, w_{13}, p_{26}, m_{26}
  552. Polygon(K_5, O_5, N_9, J_5, H_9) → poly69, k_{26}, o_{12}, n_{25}, j_{25}, h_{28}
  553. Polygon(D_8, L_8, R_9, A_{12}, L_9) → poly70, d_{27}, l_{27}, r_{28}, a_{28}, l_{28}
  554. Polygon(P_9, Z_9, E_4, B_{12}, I_8) → poly71, p_{27}, z_{14}, e_{29}, b_{28}, i_{28}
  555. Polygon(T_9, T_3, P_6, U_{11}, W_9) → poly72, t_{25}, t_{26}, p_{28}, u_{11}, w_{14}
  556. Polygon(S_8, V_9, U_9) → poly73, u_9, s_{26}, v_{14}
  557. Polygon(A_{10}, C_{10}, V_8, C_{12}, G_8) → poly74, a_{29}, c_{29}, v_{15}, c_{30}, g_{29}
  558. Polygon(W_8, T_8, B_{10}) → poly75, b_{29}, w_{15}, t_{27}
  559. Polygon(N_8, E_{10}, U_8) → poly76, u_8, n_{26}, e_{30}
  560. Polygon(D_{10}, F_{10}, Q_8, J_{12}, R_8) → poly77, d_{28}, f_{29}, q_{26}, j_{26}, r_{29}
  561. Polygon(P_8, I_{10}, J_8) → poly78, j_{27}, p_{29}, i_{29}
  562. Polygon(H_{10}, J_{10}, S_5, A_8, H_8) → poly79, h_{29}, j_{28}, s_{27}, a_{30}, h_{30}
  563. Polygon(S_9, G_{10}, K_8, K_{12}, N_5) → poly80, s_{28}, g_{30}, k_{27}, k_{28}, n_{27}
  564. Polygon(U_7, M_{10}, Z_7) → poly81, z_{15}, u_7, m_{27}
  565. Polygon(O_9, K_{10}, Q_5, I_{12}, B_8) → poly82, o_{13}, k_{29}, q_{27}, i_{30}, b_{30}
  566. Polygon(L_{10}, N_{10}, R_5, H_{12}, E_8) → poly83, l_{29}, n_{28}, r_{30}, h_{31}, e_{31}
  567. Polygon(F_{11}, I_{11}, A_2, C_1, M_{11}, L_{11}, L_2, O, C_{11}, M, F_2, E_2, F_1, I_1, J_2, I_2) → poly84, f_{30}, i_{33}, a_{31}, c_{32}, m_{29}, l_{30}, l_{31}, o_{14}, i_{31}, c_{31}, m_{28}, f_{31}, e_{32}, f_{32}, i_{32}, j_{29}
  568. Polygon(D_2, K_2, I_5, Z_3, D_7, C_7, S_2, R_1, C_2, T_1, E_9, D_9, E_5, G_{12}, J_9, I_9) → poly85, d_{29}, i_{34}, i_{35}, z_{16}, d_{31}, c_{34}, s_{29}, r_{31}, k_{30}, c_{33}, t_{28}, e_{33}, d_{30}, e_{34}, g_{31}, j_{30}
  569. Polygon(J_2, K_2, D_2, I_2) → poly86, j_{31}, k_{31}, d_{32}, i_{36}
  570. Polygon(I_9, J_9, K_9, H_9) → poly87, i_{37}, j_{32}, k_{32}, h_{32}
  571. Polygon(H_9, K_9, Q_5, I_{12}, O_9, N_9, O_5, J_5, D_5, L_5, O_{10}, N_{10}, R_5, H_{12}, L_{10}, K_{10}) → poly88, h_{33}, k_{34}, q_{28}, i_{38}, o_{16}, n_{30}, o_{17}, j_{33}, k_{33}, d_{33}, l_{32}, o_{15}, n_{29}, r_{32}, h_{34}, l_{33}
  572. Polygon(K_{10}, L_{10}, A_8, J_{10}, M_{10}, U_7, Z_7, T_7, J_8, I_{10}, H_{10}, H_8) → poly89, k_{35}, h_{36}, a_{32}, j_{35}, l_{34}, m_{30}, u_{12}, z_{17}, t_{29}, j_{34}, i_{39}, h_{35}
  573. Polygon(R, P, U, H_{11}, G_{11}, B_{11}) → poly90, r_{33}, p_{30}, u_{13}, h_{37}, g_{32}, b_{31}
  574. Polygon(F_{11}, G_{11}, H_{11}, I_{11}) → poly91, f_{33}, g_{33}, h_{38}, i_{40}
  575. Polygon(V, R, Q_1, G_{11}, F_{11}, E_{11}, O, L_{11}, M_{11}, J_{11}, K_{11}) → poly92, v_{16}, k_{36}, q_{29}, r_{34}, g_{34}, f_{34}, e_{35}, o_{18}, l_{35}, m_{31}, j_{36}
  576. Polygon(M_{11}, S_1, O_{11}, Z_5, W_5, M_2, E_1, J_{11}, C_1, I_2, D_2, B_2, R_1, C_7, B_7, T_2) → poly93, m_{32}, t_{30}, o_{19}, z_{18}, w_{16}, m_{33}, e_{36}, j_{37}, s_{30}, c_{35}, i_{41}, d_{34}, b_{32}, r_{35}, c_{36}, b_{33}
  577. Polygon(B_7, C_7, M_9, M_5, P_5, U_6, Z_6, C_3, W_{11}, A_7, D_7, A_4, Z_3, I_9, H_9, K_5, J_5, N_9) → poly94, b_{34}, n_{31}, m_{34}, m_{35}, p_{31}, u_{14}, z_{20}, c_{38}, w_{17}, a_{34}, c_{37}, d_{35}, a_{33}, z_{19}, i_{42}, h_{39}, k_{37}, j_{38}
  578. Polygon(M_9, N_9, O_9, L_9) → poly95, m_{36}, n_{32}, o_{20}, l_{36}
  579. Polygon(L_9, O_9, K_8, K_{12}, S_9, R_9, L_8, A_{12}, B_8, I_{12}, K_{10}, J_{10}, S_5, A_8, H_{10}, G_{10}) → poly96, l_{37}, g_{35}, k_{39}, k_{40}, s_{32}, r_{36}, l_{38}, a_{36}, o_{21}, b_{35}, i_{43}, k_{38}, j_{39}, s_{31}, a_{35}, h_{40}
  580. Polygon(G_{10}, H_{10}, J_{12}, F_{10}, I_{10}, P_8, J_8, O_8, U_8, E_{10}, D_{10}, R_8) → poly97, g_{36}, r_{37}, j_{41}, f_{35}, h_{41}, i_{44}, p_{32}, j_{40}, o_{22}, u_{15}, e_{37}, d_{36}
  581. Segment(E_{11}, M) → q_{30}
  582. Segment(M, H_1) → q_{31}
  583. Segment(H_1, I_1) → t_{31}
  584. Segment(I_1, O_1) → q_{32}
  585. Segment(O_1, C_1) → t_{32}
  586. Segment(C_1, S_1) → n_{33}
  587. Segment(S_1, O) → p_{33}
  588. Segment(O, E_{11}) → q_{33}
  589. Segment(B_2, T_1) → s_{33}
  590. Segment(T_1, B_5) → t_{33}
  591. Segment(B_5, G_{12}) → n_{34}
  592. Segment(G_{12}, H_5) → p_{34}
  593. Segment(H_5, J_9) → q_{34}
  594. Segment(J_9, I_9) → s_{34}
  595. Segment(I_9, Z_3) → t_{34}
  596. Segment(Z_3, A_4) → n_{35}
  597. Segment(A_4, D_7) → p_{35}
  598. Segment(D_7, C_7) → q_{35}
  599. Segment(C_7, R_1) → s_{35}
  600. Segment(R_1, B_2) → t_{35}
  601. Segment(P_1, C_1) → b_{36}
  602. Segment(C_1, A_2) → f_{36}
  603. Segment(A_2, R_1) → n_{36}
  604. Segment(R_1, S_2) → p_{36}
  605. Segment(S_2, O_{11}) → q_{36}
  606. Segment(O_{11}, O_2) → s_{36}
  607. Segment(O_2, E_1) → t_{36}
  608. Segment(E_1, P_1) → a_{37}
  609. Segment(B_{11}, O) → b_{37}
  610. Segment(O, L_2) → d_{37}
  611. Segment(L_2, V) → f_{37}
  612. Segment(B_{11}, R) → g_{37}
  613. Segment(V, R) → m_{37}
  614. Segment(D_{11}, R) → n_{37}
  615. Segment(D_{11}, U) → p_{37}
  616. Segment(R, P) → q_{37}
  617. Segment(P, U) → s_{37}
  618. Segment(V, Q_1) → t_{37}
  619. Segment(E_1, Q_1) → a_{38}
  620. Segment(E_1, M_2) → b_{38}
  621. Segment(M_2, P_2) → d_{38}
  622. Segment(P_2, V) → e_{38}
  623. Segment(U, C_{11}) → f_{38}
  624. Segment(C_{11}, M) → g_{38}
  625. Polygon(H_1, M, G_1, A_9, Z_8, R_4, T_4, F_9, E_9, B_5, T_1, K_2, I_{11}, J_2, O_1, I_1, E_2, F_2, H_{11}, D_{11}, U, L_1, G_2, H_2, K_1) → poly98, h_{42}, k_{41}, g_{40}, a_{39}, z_{21}, r_{38}, t_{38}, f_{39}, e_{39}, b_{39}, t_{39}, m_{38}, k_{42}, j_{42}, o_{23}, i_{46}, e_{40}, f_{40}, i_{45}, h_{43}, d_{39}, u_{16}, l_{39}, g_{39}, h_{44}
  626. Polygon(E_9, F_9, O_{10}, S_7, L_5, K_9, J_9, H_5, G_{12}, D_9, G_9, G_5, F_5, S_{10}, R_{10}, I_7, F_{12}, P_{10}) → poly99, e_{41}, p_{38}, o_{24}, s_{39}, l_{40}, k_{43}, j_{43}, h_{45}, g_{43}, d_{40}, f_{41}, g_{41}, g_{42}, f_{42}, s_{38}, r_{39}, i_{47}, f_{43}
  627. Polygon(O_{10}, P_{10}, H_{12}, N_{10}, Q_{10}, R_7, V_7, Q_7, Z_7, M_{10}, L_{10}, E_8) → poly100, o_{25}, e_{42}, h_{46}, n_{38}, p_{39}, q_{38}, r_{40}, v_{17}, q_{39}, z_{22}, m_{39}, l_{41}
  628. Point(e) → M_{12}
  629. Point(e_{38}) → N_{12}
  630. Polygon(V, K_{11}, A_7, H_3, W_{11}, Z_6, W_6, G_3, Q_{11}, D_6, C_6, F_3, J_{11}, N_{11}, U_5, R_2, M_{12}, D, P_2, V_5, Q_2, N_{12}, P_1, E_1, W_5, Z_5, O_2, O_{11}, B_7) → poly101, v_{18}, b_{40}, a_{40}, h_{47}, w_{19}, z_{24}, w_{20}, g_{44}, q_{40}, d_{41}, c_{39}, k_{44}, f_{44}, n_{39}, u_{17}, r_{41}, m_{40}, d_{42}, p_{41}, v_{19}, q_{41}, n_{40}, j_{44}, p_{40}, e_{43}, w_{18}, z_{23}, o_{26}, o_{27}
  631. Polygon(V, K_{11}, N_{12}, J_{11}, P_1, E_1, W_5, Z_5, U_5, V_5, Q_2) → poly102, v_{20}, q_{42}, n_{41}, k_{45}, j_{45}, p_{42}, e_{44}, w_{21}, z_{25}, u_{18}, v_{21}
  632. Polygon(U_5, Z_5, V_6, W_6, G_3, Q_{11}, D_6, C_6, F_3, M_{12}, O_2, O_{11}, B_7, A_7, H_3, W_{11}, Z_6, U_6) → poly103, u_{19}, u_{20}, v_{22}, w_{23}, g_{45}, q_{43}, d_{43}, c_{40}, f_{45}, m_{41}, z_{26}, o_{28}, o_{29}, b_{41}, a_{41}, h_{48}, w_{22}, z_{27}
  633. Polygon(V_6, U_6, N_5, K_{12}, G_{10}, F_{10}, Q_8, J_{12}, D_{10}, E_{10}, N_8, U_8, W_3, M_8, W_8, B_{10}, C_{10}, V_8, C_{12}, A_{10}, Z_9, E_4, B_{12}, P_5, P_9, Q_9, C_8, J_4, Q_6, T_6, P_3, Z_{11}, M_9, L_9, D_8, A_{12}, R_9, S_9) → poly104, v_{23}, s_{40}, n_{42}, k_{46}, g_{46}, f_{46}, q_{44}, j_{46}, d_{45}, e_{45}, n_{43}, u_{21}, u_{22}, m_{43}, w_{25}, b_{42}, c_{41}, v_{24}, c_{42}, a_{43}, z_{28}, e_{46}, w_{24}, b_{43}, p_{44}, q_{45}, c_{43}, j_{47}, q_{46}, t_{40}, p_{45}, z_{29}, p_{43}, m_{42}, l_{42}, d_{44}, a_{42}, r_{42}
  634. Polygon(N_{12}, V_5, V_6, K_4, Z_{11}, T_6, S_6, R_3, S_{11}, H_6, G_6, L_3, U_5, P_{11}, A_6, B_6, W_2, E_3, R_2, M_{12}, C_6, D_6, V_2, Q_{11}, W_6) → poly105, n_{44}, w_{26}, v_{27}, k_{47}, z_{30}, t_{41}, s_{41}, r_{44}, s_{42}, h_{49}, g_{47}, v_{25}, l_{43}, p_{46}, a_{44}, b_{44}, w_{27}, e_{47}, u_{23}, r_{43}, m_{44}, c_{44}, d_{46}, v_{26}, q_{47}
  635. Polygon(T_6, Q_6, V_9, W_9, T_9, U_{11}, P_6, O_6, O_4, V_{11}, R_6, S_6, V_3, J_4, Q_9, P_9, I_8, B_{12}, Z_9, A_{10}) → poly106, t_{42}, a_{45}, v_{29}, w_{28}, t_{43}, u_{24}, p_{48}, o_{30}, o_{31}, v_{30}, r_{45}, q_{48}, s_{43}, v_{28}, j_{48}, q_{49}, p_{47}, i_{48}, b_{45}, z_{31}
  636. Polygon(A_{10}, G_8, C_{12}, C_{10}, B_{10}, T_8, W_8, F_8, U_9, V_9) → poly107, a_{46}, v_{31}, g_{48}, c_{45}, c_{46}, b_{46}, t_{44}, w_{29}, f_{47}, u_{25}
  637. Polygon(L_1, W_4, N_1, B_9, C_9, Z_8, A_9, P_4, G_1, H_2, G_2) → poly108, l_{44}, g_{50}, n_{45}, w_{30}, b_{47}, c_{47}, z_{32}, a_{47}, p_{49}, g_{49}, h_{50}
  638. Polygon(C_9, V_4, F_5, G_9, F_9, Q_4, T_4, Z_8, S_4, W_{10}, V_{10}, N_7, E_{12}, T_{10}, S_{10}, A_5) → poly109, c_{48}, a_{48}, f_{48}, g_{51}, f_{49}, q_{50}, t_{46}, z_{33}, v_{32}, s_{44}, w_{31}, v_{33}, n_{46}, e_{48}, t_{45}, s_{45}
  639. Point(e_9) → P_{12}
  640. Intersect(l, t_9) → O_{12}
  641. Polygon(O_{12}, Q_{10}, L_7, G_7, P_{10}, W_7, F_{12}, R_{10}, S_{10}, T_{10}, P_{12}, H_7) → poly110, o_{32}, h_{51}, l_{45}, g_{52}, q_{51}, p_{50}, w_{32}, f_{50}, r_{46}, s_{46}, t_{47}, p_{51}
  642. Polygon(N_3, E_3, I_3, B_6, A_6, B_3, P_{11}, G_6, H_6, E_6, F_6) → poly111, n_{47}, f_{51}, i_{49}, e_{49}, b_{48}, a_{49}, b_{49}, p_{52}, g_{53}, h_{52}, e_{50}
  643. Polygon(H_6, A_3, N_6, B_4, T_{11}, L_6, K_6, H_4, R_{11}, E_6, S_{11}, S_6, R_6, G_4, V_{11}, O_6, P_6, M_6) → poly112, h_{53}, m_{45}, n_{48}, b_{50}, t_{48}, l_{46}, k_{48}, h_{54}, r_{48}, e_{51}, a_{50}, s_{47}, s_{48}, r_{47}, g_{54}, v_{34}, o_{33}, p_{53}
  644. Polygon(M_6, P_6, T_3, U_{11}, W_9, V_9, S_8, U_9, S_3, C_4) → poly113, m_{46}, c_{49}, p_{54}, t_{49}, u_{26}, w_{33}, v_{35}, s_{49}, u_{27}, s_{50}
  645. Polygon(N_3, F_6, M_6, D_4, C_4, M_4, I_6, J_6, L_4, I_4, E_6, O_3, R_{11}, K_6, L_6, K_3, T_{11}, N_6) → poly114, n_{49}, n_{50}, m_{47}, d_{47}, c_{50}, m_{48}, i_{50}, j_{49}, l_{48}, i_{51}, f_{52}, e_{52}, o_{34}, r_{49}, k_{49}, l_{47}, k_{50}, t_{50}
  646. Polygon(M_7, Z_{10}, V_{10}, W_{10}, F_7, S_4, C_9, B_9, Z_4, W_4, A_{11}, J_7, O_7, L_7, P_{12}, T_{10}, P_7, E_{12}) → poly115, m_{49}, e_{53}, v_{36}, w_{34}, f_{53}, s_{51}, c_{51}, b_{51}, z_{35}, w_{35}, z_{34}, a_{51}, j_{50}, o_{35}, l_{49}, p_{55}, t_{51}, p_{56}
  647. Polygon(M_7, K, O_7, A_{11}, Z_{10}, E_7) → poly116, m_{50}, k_{51}, o_{36}, a_{52}, z_{36}, e_{54}
  648. Polygon(I_4, J_6, I_6, N_4, M_4, G) → poly117, i_{52}, j_{51}, i_{53}, n_{51}, m_{51}, g_{55}
  649. Segment(Z_3, H_3) → d_{48}
  650. Segment(H_3, W_{11}) → d_{49}
  651. Segment(Z_3, I_5) → d_{50}
  652. Segment(I_5, J_5) → l_{50}
  653. Segment(J_5, O_5) → r_{50}
  654. Segment(O_5, P_5) → d_{51}
  655. Segment(P_5, W_3) → l_{51}
  656. Segment(W_3, W_{11}) → r_{51}
  657. Segment(I_{12}, D_8) → b_{52}
  658. Segment(I_{12}, Q_5) → c_{52}
  659. Segment(A_8, Q_5) → d_{52}
  660. Segment(A_{12}, D_8) → j_{52}
  661. Segment(N_5, A_{12}) → k_{52}
  662. Segment(N_5, K_{12}) → l_{52}
  663. Segment(K_{12}, H_8) → m_{52}
  664. Segment(H_8, A_8) → n_{52}
  665. Segment(J_8, F_{10}) → q_{52}
  666. Segment(F_{10}, Q_8) → r_{52}
  667. Segment(Q_8, J_{12}) → s_{52}
  668. Segment(J_{12}, E_{10}) → t_{52}
  669. Segment(E_{10}, N_8) → a_{53}
  670. Segment(N_8, U_8) → b_{53}
  671. Segment(U_8, J_8) → c_{53}
  672. Segment(C_2, I_1) → d_{53}
  673. Segment(I_1, F_1) → j_{53}
  674. Segment(F_1, G_1) → k_{53}
  675. Segment(G_1, P_4) → l_{53}
  676. Segment(P_4, T_4) → m_{53}
  677. Segment(T_4, Q_4) → n_{53}
  678. Segment(Q_4, T_1) → q_{53}
  679. Segment(T_1, C_2) → r_{53}
  680. Segment(K_1, L_1) → s_{53}
  681. Segment(K_1, G_1) → t_{53}
  682. Segment(G_1, Z_4) → a_{54}
  683. Segment(Z_4, W_4) → b_{54}
  684. Segment(W_4, L_1) → c_{54}
  685. Segment(L_1, N_1) → d_{54}
  686. Segment(N_1, M) → f_{54}
  687. Segment(L_1, U) → i_{54}
  688. Segment(E_5, F_5) → j_{54}
  689. Segment(F_5, A_5) → k_{54}
  690. Segment(A_5, F_{12}) → l_{54}
  691. Segment(F_{12}, W_7) → m_{54}
  692. Segment(W_7, L_5) → n_{54}
  693. Segment(L_5, D_5) → q_{54}
  694. Segment(D_5, G_{12}) → r_{54}
  695. Segment(G_{12}, E_5) → s_{54}
  696. Segment(K_5, L_5) → t_{54}
  697. Segment(L_5, S_7) → a_{55}
  698. Segment(S_7, H_{12}) → b_{55}
  699. Segment(H_{12}, E_8) → c_{55}
  700. Segment(E_8, I_{12}) → d_{55}
  701. Segment(I_{12}, B_8) → e_{55}
  702. Segment(B_8, J_5) → f_{55}
  703. Segment(J_5, K_5) → h_{55}
  704. Segment(S_4, R_4) → i_{55}
  705. Segment(R_4, T_4) → j_{55}
  706. Segment(T_4, G_5) → k_{55}
  707. Segment(G_5, F_5) → l_{55}
  708. Segment(F_5, P_7) → m_{55}
  709. Segment(S_4, F_7) → n_{55}
  710. Segment(F_7, E_{12}) → q_{55}
  711. Segment(E_{12}, P_7) → r_{55}
  712. Segment(L_7, I_7) → s_{55}
  713. Segment(I_7, F_{12}) → t_{55}
  714. Segment(F_{12}, R_7) → a_{56}
  715. Segment(R_7, O_{12}) → b_{56}
  716. Segment(O_{12}, L_7) → c_{56}
  717. Segment(T_2, W_{11}) → d_{56}
  718. Segment(W_{11}, C_3) → e_{56}
  719. Segment(C_3, Q_{11}) → f_{56}
  720. Segment(Q_{11}, V_2) → g_{56}
  721. Segment(V_2, M_{12}) → h_{56}
  722. Segment(M_{12}, R_2) → i_{56}
  723. Segment(R_2, O_{11}) → j_{56}
  724. Segment(O_{11}, T_2) → k_{56}
  725. Segment(K_4, P_5) → l_{56}
  726. Segment(P_5, M_5) → m_{56}
  727. Segment(M_5, A_{12}) → n_{56}
  728. Segment(A_{12}, L_8) → q_{56}
  729. Segment(L_8, J_4) → r_{56}
  730. Segment(J_4, V_3) → s_{56}
  731. Segment(V_3, Z_{11}) → t_{56}
  732. Segment(Z_{11}, K_4) → a_{57}
  733. Segment(I_8, K_{12}) → b_{57}
  734. Segment(K_{12}, K_8) → c_{57}
  735. Segment(K_8, J_{12}) → d_{57}
  736. Segment(J_{12}, R_8) → e_{57}
  737. Segment(R_8, C_{12}) → f_{57}
  738. Segment(C_{12}, G_8) → g_{57}
  739. Segment(G_8, B_{12}) → h_{57}
  740. Segment(B_{12}, I_8) → i_{57}
  741. Segment(T_8, U_8) → j_{57}
  742. Segment(T_8, W_8) → k_{57}
  743. Segment(W_8, M_8) → l_{57}
  744. Segment(M_8, U_8) → m_{57}
  745. Segment(P_{11}, W_2) → n_{57}
  746. Segment(W_2, E_3) → p_{57}
  747. Segment(E_3, N_{12}) → q_{57}
  748. Segment(N_{12}, V_5) → r_{57}
  749. Segment(N_{12}, Q_2) → s_{57}
  750. Segment(Q_2, M_{12}) → t_{57}
  751. Segment(M_{12}, F_3) → a_{58}
  752. Segment(F_3, B_6) → b_{58}
  753. Segment(B_6, E_3) → c_{58}
  754. Segment(B_3, Q_{11}) → d_{58}
  755. Segment(Q_{11}, G_3) → e_{58}
  756. Segment(G_3, Z_{11}) → f_{58}
  757. Segment(Z_{11}, P_3) → g_{58}
  758. Segment(P_3, S_{11}) → h_{58}
  759. Segment(S_{11}, A_3) → i_{58}
  760. Segment(A_3, P_{11}) → j_{58}
  761. Segment(P_{11}, B_3) → k_{58}
  762. Segment(G_4, J_4) → l_{58}
  763. Segment(J_4, C_8) → m_{58}
  764. Segment(C_8, B_{12}) → n_{58}
  765. Segment(B_{12}, E_4) → p_{58}
  766. Segment(E_4, U_{11}) → q_{58}
  767. Segment(U_{11}, T_3) → r_{58}
  768. Segment(T_3, V_{11}) → s_{58}
  769. Segment(V_{11}, G_4) → t_{58}
  770. Segment(S_8, C_{12}) → a_{59}
  771. Segment(U_9, S_8) → b_{59}
  772. Segment(C_{12}, V_8) → c_{59}
  773. Segment(V_8, W_8) → d_{59}
  774. Segment(W_8, U_9) → e_{59}
  775. Segment(C_4, B_4) → f_{59}
  776. Segment(B_4, T_{11}) → g_{59}
  777. Segment(T_{11}, N_4) → h_{59}
  778. Segment(N_4, M_4) → i_{59}
  779. Segment(M_4, C_4) → j_{59}
  780. Segment(H_4, I_4) → k_{59}
  781. Segment(H_4, R_{11}) → l_{59}
  782. Segment(R_{11}, I_3) → m_{59}
  783. Segment(I_3, N_3) → n_{59}
  784. Segment(N_3, I_4) → p_{59}
  785. Segment(N_3, L_3) → q_{59}
  786. Segment(L_3, P_{11}) → r_{59}
  787. Segment(O_3, R_{11}) → s_{59}
  788. Segment(R_{11}, K_3) → t_{59}
  789. Segment(K_3, T_{11}) → a_{60}
  790. Segment(T_{11}, O_4) → b_{60}
  791. Segment(O_4, V_{11}) → c_{60}
  792. Segment(V_{11}, R_3) → d_{60}
  793. Segment(R_3, S_{11}) → e_{60}
  794. Segment(S_{11}, O_3) → f_{60}
  795. Segment(U_{11}, D_4) → g_{60}
  796. Segment(D_4, C_4) → h_{60}
  797. Segment(C_4, U_9) → i_{60}
  798. Segment(U_9, T_9) → j_{60}
  799. Segment(T_9, U_{11}) → k_{60}
  800. Segment(W_4, V_4) → l_{60}
  801. Segment(V_4, S_4) → m_{60}
  802. Segment(S_4, E_7) → n_{60}
  803. Segment(E_7, M_7) → p_{60}
  804. Segment(O_7, N_7) → q_{60}
  805. Segment(N_7, E_{12}) → r_{60}
  806. Segment(E_{12}, H_7) → s_{60}
  807. Segment(H_7, L_7) → t_{60}
  808. Segment(L_7, O_7) → a_{61}
  809. Segment(M_7, W_4) → b_{61}
  810. Segment(M_7, J_7) → c_{61}
  811. Segment(J_7, O_7) → d_{61}
  812. Segment(O_{12}, R_5) → e_{61}
  813. Segment(R_5, H_{12}) → f_{61}
  814. Segment(H_{12}, L_{10}) → g_{61}
  815. Segment(L_{10}, U_7) → h_{61}
  816. Segment(U_7, Z_7) → i_{61}
  817. Segment(Z_7, O_{12}) → j_{61}
  818. Segment(Z_7, S_5) → k_{61}
  819. Segment(S_5, A_8) → l_{61}
  820. Segment(A_8, P_8) → m_{61}
  821. Segment(P_8, J_8) → n_{61}
  822. Segment(J_8, Z_7) → p_{61}
  823. Intersect(k_9, b_{18}) → Q_{12}
  824. Intersect(m_{50}, k_{51}) → R_{12}
  825. Segment(Q_{12}, R_{12}) → q_{61}
  826. Intersect(i_9, a_{18}) → S_{12}
  827. Segment(R_{12}, S_{12}) → r_{61}
  828. Intersect(d_4, t_{14}) → T_{12}
  829. Intersect(l_4, e_{15}) → U_{12}
  830. Segment(T_{12}, U_{12}) → s_{61}
  831. Intersect(r_5, j_{15}) → V_{12}
  832. Intersect(m_{51}, g_{55}) → W_{12}
  833. Segment(V_{12}, W_{12}) → t_{61}
  834. Intersect(m_5, h_{15}) → Z_{12}
  835. Segment(W_{12}, Z_{12}) → a_{62}
  836. Intersect(r_5, j_{15}) → A_{13}
  837. Intersect(r_5, h_{15}) → B_{13}
  838. Segment(A_{13}, B_{13}) → b_{62}
  839. Intersect(m_5, h_{15}) → C_{13}
  840. Segment(B_{13}, C_{13}) → c_{62}

AI Drawing Prompt Reference

Draw a geometric tiling pattern based on the Pythagorean theorem, creating a continuous design through combining different triangles. Start by drawing a line segment, then draw two perpendicular segments from each endpoint of the line segment. Mark the intersection points and repeat the process to form multiple triangles. Connect the intersection points with line segments to create a complex geometric pattern, demonstrating rotational symmetry and the application of the Pythagorean theorem.
The prompt above was compiled from the original drawing commands and is for reference only.