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Discovering Symmetry in Periodic Tiling

Discovering Symmetry in Periodic Tiling
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2013-02-25 18:26
PolygonTransformationGeometric Construction
This example demonstrates how to identify symmetry in periodic tilings. It involves core mathematical concepts like symmetry, and the basic shapes of lattices such as parallelograms, rectangles, rhombuses, squares, or hexagons. GeoGebra commands and objects used include Polygon, LineBisector, Intersect, Point, Line, Mirror, Segment, Rotate, Vector, and Translate. Suitable for high school mathematics education or geometry learning, helping students understand and practice symmetry and tiling patterns.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 6) → veelhoek1, a, F, b, c, d, e, f, C, D, E
  2. LineBisector(d) → g
  3. LineBisector(c) → h
  4. Intersect(g, h) → G
  5. Polygon(F, G, A) → veelhoek2, a_1, f_1, g_1
  6. Point(f) → H
  7. Point(f_1) → I
  8. Polygon(H, A, I) → veelhoek3, i, h_1, a_2
  9. Line(D, A) → j
  10. Mirror(F, j) → F'
  11. Mirror(G, j) → G'
  12. Mirror(A, j) → A'
  13. Polygon(F', G', A') → veelhoek2', a', f', g'
  14. Mirror(H, j) → H'
  15. Mirror(A, j) → A'_1
  16. Mirror(I, j) → I'
  17. Polygon(H', A'_1, I') → veelhoek3', i', h', a'_1
  18. Mirror(F, j) → F'_1
  19. Mirror(A, j) → A'_2
  20. Segment(F'_1, A'_2) → f'_1
  21. Rotate(F, 120*°, G) → F'_2
  22. Rotate(G, 120*°, G) → G'_1
  23. Rotate(A, 120*°, G) → A'_3
  24. Polygon(F'_2, G'_1, A'_3) → veelhoek2'_1, a'_3, f'_2, g'_1
  25. Rotate(H, 120*°, G) → H'_1
  26. Rotate(A, 120*°, G) → A'_4
  27. Rotate(I, 120*°, G) → I'_1
  28. Polygon(H'_1, A'_4, I'_1) → veelhoek3'_1, i'_1, h'_1, a'_4
  29. Rotate(F', 120*°, G) → F''
  30. Rotate(G', 120*°, G) → G''
  31. Rotate(A', 120*°, G) → A''
  32. Polygon(F'', G'', A'') → veelhoek2'', a'', f'', g''
  33. Rotate(H', 120*°, G) → H''
  34. Rotate(A'_1, 120*°, G) → J
  35. Rotate(I', 120*°, G) → I''
  36. Polygon(H'', J, I'') → veelhoek3'', i'', h'', j_1
  37. Rotate(F, 120*°, G) → F'_3
  38. Rotate(A, 120*°, G) → A'_5
  39. Segment(F'_3, A'_5) → f'_3
  40. Rotate(A, 120*°, G) → A'_6
  41. Rotate(B, 120*°, G) → B'
  42. Segment(A'_6, B') → a'_2
  43. Rotate(F'_1, 120*°, G) → K
  44. Rotate(A'_2, 120*°, G) → L
  45. Segment(K, L) → k
  46. Rotate(F'_2, 120*°, G) → M
  47. Rotate(G'_1, 120*°, G) → N
  48. Rotate(A'_3, 120*°, G) → O
  49. Polygon(M, N, O) → veelhoek4, o, m, n
  50. Rotate(H'_1, 120*°, G) → P
  51. Rotate(A'_4, 120*°, G) → Q
  52. Rotate(I'_1, 120*°, G) → R
  53. Polygon(P, Q, R) → veelhoek5, r, p, q
  54. Rotate(F'', 120*°, G) → F'''
  55. Rotate(G'', 120*°, G) → G'''
  56. Rotate(A'', 120*°, G) → A'''
  57. Polygon(F''', G''', A''') → veelhoek2''', a''', f''', g'''
  58. Rotate(H'', 120*°, G) → H'''
  59. Rotate(J, 120*°, G) → J'
  60. Rotate(I'', 120*°, G) → I'''
  61. Polygon(H''', J', I''') → veelhoek3''', i''', h''', j'
  62. Rotate(C, 120*°, G) → C'
  63. Rotate(D, 120*°, G) → D'
  64. Segment(C', D') → c'
  65. Rotate(B, 120*°, G) → B'_1
  66. Rotate(C, 120*°, G) → C'_1
  67. Segment(B'_1, C'_1) → b'
  68. Rotate(F', 120*°, G) → F''_1
  69. Rotate(G', 120*°, G) → G''_1
  70. Segment(F''_1, G''_1) → a''_1
  71. Rotate(F'_3, 120*°, G) → S
  72. Rotate(A'_5, 120*°, G) → T
  73. Segment(S, T) → l
  74. Rotate(A'_6, 120*°, G) → U
  75. Rotate(B', 120*°, G) → B''
  76. Segment(U, B'') → s
  77. Rotate(K, 120*°, G) → K'
  78. Rotate(L, 120*°, G) → L'
  79. Segment(K', L') → k'
  80. Rotate(H', 120*°, G) → H''_1
  81. Rotate(F'_1, 120*°, G) → V
  82. Vector(D, F) → u
  83. Vector(B, F) → v
  84. Translate(veelhoek1, u) → veelhoek1'
  85. Translate(F, u) → F'_4
  86. Translate(G, u) → G'_2
  87. Translate(A, u) → A'_7
  88. Polygon(F'_4, G'_2, A'_7) → veelhoek2'_2, a'_7, f'_4, g'_2
  89. Translate(H, u) → H'_2
  90. Translate(A, u) → A'_8
  91. Translate(I, u) → I'_2
  92. Polygon(H'_2, A'_8, I'_2) → veelhoek3'_2, i'_2, h'_2, a'_8
  93. Translate(F', u) → F''_2
  94. Translate(G', u) → G''_2
  95. Translate(A', u) → A''_1
  96. Polygon(F''_2, G''_2, A''_1) → veelhoek2''_1, a''_2, f''_2, g''_2
  97. Translate(H', u) → H''_2
  98. Translate(A'_1, u) → W
  99. Translate(I', u) → I''_1
  100. Polygon(H''_2, W, I''_1) → veelhoek3''_1, i''_1, h''_2, w
  101. Translate(F'_2, u) → Z
  102. Translate(G'_1, u) → A_1
  103. Translate(A'_3, u) → B_1
  104. Polygon(Z, A_1, B_1) → veelhoek6, b_1, z, a_3
  105. Translate(H'_1, u) → C_1
  106. Translate(A'_4, u) → D_1
  107. Translate(I'_1, u) → E_1
  108. Polygon(C_1, D_1, E_1) → veelhoek7, e_1, c_1, d_1
  109. Translate(F'', u) → F'''_1
  110. Translate(G'', u) → G'''_1
  111. Translate(A'', u) → A'''_1
  112. Polygon(F'''_1, G'''_1, A'''_1) → veelhoek2'''_1, a'''_1, f'''_1, g'''_1
  113. Translate(H'', u) → H'''_1
  114. Translate(J, u) → J'_1
  115. Translate(I'', u) → I'''_1
  116. Polygon(H'''_1, J'_1, I'''_1) → veelhoek3'''_1, i'''_1, h'''_1, j'_1
  117. Translate(M, u) → M'
  118. Translate(N, u) → N'
  119. Translate(O, u) → O'
  120. Polygon(M', N', O') → veelhoek4', o', m', n'
  121. Translate(P, u) → P'
  122. Translate(Q, u) → Q'
  123. Translate(R, u) → R'
  124. Polygon(P', Q', R') → veelhoek5', r', p', q'
  125. Translate(F''', u) → F_1
  126. Translate(G''', u) → G_1
  127. Translate(A''', u) → H_1
  128. Polygon(F_1, G_1, H_1) → veelhoek8, h_2, f_2, g_2
  129. Translate(H''', u) → I_1
  130. Translate(J', u) → J''
  131. Translate(I''', u) → J_1
  132. Polygon(I_1, J'', J_1) → veelhoek9, j_2, i_1, j''
  133. Translate(F'_1, u) → K_1
  134. Translate(A'_2, u) → L_1
  135. Segment(K_1, L_1) → t
  136. Translate(F'_3, u) → M_1
  137. Translate(A'_5, u) → N_1
  138. Segment(M_1, N_1) → k_1
  139. Translate(A'_6, u) → O_1
  140. Translate(B', u) → B''_1
  141. Segment(O_1, B''_1) → l_1
  142. Translate(K, u) → K'_1
  143. Translate(L, u) → L'_1
  144. Segment(K'_1, L'_1) → k'_1
  145. Translate(C', u) → C''
  146. Translate(D', u) → D''
  147. Segment(C'', D'') → c''
  148. Translate(B'_1, u) → P_1
  149. Translate(C'_1, u) → Q_1
  150. Segment(P_1, Q_1) → b''
  151. Translate(F''_1, u) → R_1
  152. Translate(G''_1, u) → S_1
  153. Segment(R_1, S_1) → m_1
  154. Translate(S, u) → S'
  155. Translate(T, u) → T'
  156. Segment(S', T') → l'
  157. Translate(U, u) → U'
  158. Translate(B'', u) → B'''
  159. Segment(U', B''') → s'
  160. Translate(K', u) → K''
  161. Translate(L', u) → L''
  162. Segment(K'', L'') → k''
  163. Translate(v, u) → v'
  164. Translate(H''_1, u) → T_1
  165. Translate(V, u) → V'
  166. Translate(veelhoek1, v') → veelhoek1'_1
  167. Translate(F, v') → F'_5
  168. Translate(G, v') → G'_3
  169. Translate(A, v') → A'_9
  170. Polygon(F'_5, G'_3, A'_9) → veelhoek2'_3, a'_9, f'_5, g'_3
  171. Translate(H, v') → H'_3
  172. Translate(A, v') → A'_{10}
  173. Translate(I, v') → I'_3
  174. Polygon(H'_3, A'_{10}, I'_3) → veelhoek3'_3, i'_3, h'_3, a'_{10}
  175. Translate(F', v') → F''_3
  176. Translate(G', v') → G''_3
  177. Translate(A', v') → A''_2
  178. Polygon(F''_3, G''_3, A''_2) → veelhoek2''_2, a''_3, f''_3, g''_3
  179. Translate(H', v') → H''_3
  180. Translate(A'_1, v') → U_1
  181. Translate(I', v') → I''_2
  182. Polygon(H''_3, U_1, I''_2) → veelhoek3''_2, i''_2, h''_3, u_1
  183. Translate(F'_2, v') → V_1
  184. Translate(G'_1, v') → W_1
  185. Translate(A'_3, v') → Z_1
  186. Polygon(V_1, W_1, Z_1) → veelhoek10, z_1, v_1, w_1
  187. Translate(H'_1, v') → A_2
  188. Translate(A'_4, v') → B_2
  189. Translate(I'_1, v') → C_2
  190. Polygon(A_2, B_2, C_2) → veelhoek11, c_2, a_4, b_2
  191. Translate(F'', v') → F'''_2
  192. Translate(G'', v') → G'''_2
  193. Translate(A'', v') → A'''_2
  194. Polygon(F'''_2, G'''_2, A'''_2) → veelhoek2'''_2, a'''_2, f'''_2, g'''_2
  195. Translate(H'', v') → H'''_2
  196. Translate(J, v') → J'_2
  197. Translate(I'', v') → I'''_2
  198. Polygon(H'''_2, J'_2, I'''_2) → veelhoek3'''_2, i'''_2, h'''_2, j'_2
  199. Translate(M, v') → M'_1
  200. Translate(N, v') → N'_1
  201. Translate(O, v') → O'_1
  202. Polygon(M'_1, N'_1, O'_1) → veelhoek4'_1, o'_1, m'_1, n'_1
  203. Translate(P, v') → P'_1
  204. Translate(Q, v') → Q'_1
  205. Translate(R, v') → R'_1
  206. Polygon(P'_1, Q'_1, R'_1) → veelhoek5'_1, r'_1, p'_1, q'_1
  207. Translate(F''', v') → D_2
  208. Translate(G''', v') → E_2
  209. Translate(A''', v') → F_2
  210. Polygon(D_2, E_2, F_2) → veelhoek12, f_3, d_2, e_2
  211. Translate(H''', v') → G_2
  212. Translate(J', v') → J''_1
  213. Translate(I''', v') → H_2
  214. Polygon(G_2, J''_1, H_2) → veelhoek13, h_3, g_3, j''_1
  215. Translate(H'''_1, v') → I_2
  216. Translate(J'_1, v') → J_2
  217. Translate(F'_1, v') → L_2
  218. Translate(A'_2, v') → M_2
  219. Segment(L_2, M_2) → n_1
  220. Translate(F'_3, v') → N_2
  221. Translate(A'_5, v') → O_2
  222. Segment(N_2, O_2) → p_1
  223. Translate(A'_6, v') → P_2
  224. Translate(B', v') → B''_2
  225. Segment(P_2, B''_2) → q_1
  226. Translate(K, v') → K'_2
  227. Translate(L, v') → L'_2
  228. Segment(K'_2, L'_2) → k'_2
  229. Translate(C', v') → C''_1
  230. Translate(D', v') → D''_1
  231. Segment(C''_1, D''_1) → c''_1
  232. Translate(B'_1, v') → Q_2
  233. Translate(C'_1, v') → R_2
  234. Segment(Q_2, R_2) → b''_1
  235. Translate(F''_1, v') → S_2
  236. Translate(G''_1, v') → T_2
  237. Segment(S_2, T_2) → r_1
  238. Translate(S, v') → S'_1
  239. Translate(T, v') → T'_1
  240. Segment(S'_1, T'_1) → l'_1
  241. Translate(U, v') → U'_1
  242. Translate(B'', v') → B'''_1
  243. Segment(U'_1, B'''_1) → s'_1
  244. Translate(K', v') → K''_1
  245. Translate(L', v') → L''_1
  246. Segment(K''_1, L''_1) → k''_1
  247. Translate(D_1, v') → U_2
  248. Translate(A'''_1, v') → W_2
  249. Translate(F'''_1, v') → Z_2
  250. Segment(W_2, Z_2) → t_1
  251. Translate(O_1, v') → A_3
  252. Translate(B''_1, v') → B_3
  253. Segment(A_3, B_3) → l_2
  254. Translate(K'_1, v') → C_3
  255. Translate(L'_1, v') → D_3
  256. Segment(C_3, D_3) → m_2
  257. Translate(H''_1, v') → E_3
  258. Translate(V, v') → V'_1
  259. Translate(B_1, v') → F_3
  260. Translate(M', v') → M''
  261. Translate(N_1, v') → G_3
  262. Translate(P_1, v') → H_3
  263. Translate(R_1, v') → I_3
  264. Translate(S', v') → S''
  265. Translate(T_1, v') → J_3
  266. Translate(V', v') → V''
  267. Vector(C, O') → s_1
  268. Translate(veelhoek1, s_1) → veelhoek1'_2
  269. Translate(F, s_1) → F'_6
  270. Translate(G, s_1) → G'_4
  271. Translate(A, s_1) → A'_{11}
  272. Polygon(F'_6, G'_4, A'_{11}) → veelhoek2'_4, a'_{11}, f'_6, g'_4
  273. Translate(H, s_1) → H'_4
  274. Translate(A, s_1) → A'_{12}
  275. Translate(I, s_1) → I'_4
  276. Polygon(H'_4, A'_{12}, I'_4) → veelhoek3'_4, i'_4, h'_4, a'_{12}
  277. Translate(F', s_1) → F''_4
  278. Translate(G', s_1) → G''_4
  279. Translate(A', s_1) → A''_3
  280. Polygon(F''_4, G''_4, A''_3) → veelhoek2''_3, a''_4, f''_4, g''_4
  281. Translate(H', s_1) → H''_4
  282. Translate(A'_1, s_1) → K_2
  283. Translate(I', s_1) → I''_3
  284. Polygon(H''_4, K_2, I''_3) → veelhoek3''_3, i''_3, h''_4, k_2
  285. Translate(F'_2, s_1) → V_2
  286. Translate(G'_1, s_1) → K_3
  287. Translate(A'_3, s_1) → L_3
  288. Polygon(V_2, K_3, L_3) → veelhoek14, l_3, v_2, k_3
  289. Translate(H'_1, s_1) → M_3
  290. Translate(A'_4, s_1) → N_3
  291. Translate(I'_1, s_1) → O_3
  292. Polygon(M_3, N_3, O_3) → veelhoek15, o_3, m_3, n_3
  293. Translate(F'', s_1) → F'''_3
  294. Translate(G'', s_1) → G'''_3
  295. Translate(A'', s_1) → A'''_3
  296. Polygon(F'''_3, G'''_3, A'''_3) → veelhoek2'''_3, a'''_3, f'''_3, g'''_3
  297. Translate(H'', s_1) → H'''_3
  298. Translate(J, s_1) → J'_3
  299. Translate(I'', s_1) → I'''_3
  300. Polygon(H'''_3, J'_3, I'''_3) → veelhoek3'''_3, i'''_3, h'''_3, j'_3
  301. Translate(M, s_1) → M'_2
  302. Translate(N, s_1) → N'_2
  303. Translate(O, s_1) → O'_2
  304. Polygon(M'_2, N'_2, O'_2) → veelhoek4'_2, o'_2, m'_2, n'_2
  305. Translate(P, s_1) → P'_2
  306. Translate(Q, s_1) → Q'_2
  307. Translate(R, s_1) → R'_2
  308. Polygon(P'_2, Q'_2, R'_2) → veelhoek5'_2, r'_2, p'_2, q'_2
  309. Translate(F''', s_1) → P_3
  310. Translate(G''', s_1) → Q_3
  311. Translate(A''', s_1) → R_3
  312. Polygon(P_3, Q_3, R_3) → veelhoek16, r_3, p_3, q_3
  313. Translate(H''', s_1) → S_3
  314. Translate(J', s_1) → J''_2
  315. Translate(I''', s_1) → T_3
  316. Polygon(S_3, J''_2, T_3) → veelhoek17, t_3, s_3, j''_2
  317. Translate(veelhoek1', s_1) → veelhoek1''
  318. Translate(F'_4, s_1) → U_3
  319. Translate(G'_2, s_1) → V_3
  320. Translate(A'_7, s_1) → W_3
  321. Polygon(U_3, V_3, W_3) → veelhoek18, w_3, u_3, v_3
  322. Translate(H'_2, s_1) → Z_3
  323. Translate(A'_8, s_1) → A_4
  324. Translate(I'_2, s_1) → B_4
  325. Polygon(Z_3, A_4, B_4) → veelhoek19, b_4, z_3, a_5
  326. Translate(F''_2, s_1) → C_4
  327. Translate(G''_2, s_1) → D_4
  328. Translate(A''_1, s_1) → E_4
  329. Polygon(C_4, D_4, E_4) → veelhoek20, e_4, c_4, d_4
  330. Translate(H''_2, s_1) → F_4
  331. Translate(W, s_1) → W'
  332. Translate(I''_1, s_1) → G_4
  333. Polygon(F_4, W', G_4) → veelhoek21, g_4, f_4, w'
  334. Translate(Z, s_1) → Z'
  335. Translate(A_1, s_1) → H_4
  336. Translate(B_1, s_1) → I_4
  337. Polygon(Z', H_4, I_4) → veelhoek6', i_4, z', h_4
  338. Translate(C_1, s_1) → J_4
  339. Translate(D_1, s_1) → K_4
  340. Translate(E_1, s_1) → L_4
  341. Polygon(J_4, K_4, L_4) → veelhoek7', l_4, j_4, k_4
  342. Translate(F'''_1, s_1) → M_4
  343. Translate(G'''_1, s_1) → N_4
  344. Translate(A'''_1, s_1) → O_4
  345. Polygon(M_4, N_4, O_4) → veelhoek22, o_4, m_4, n_4
  346. Translate(H'''_1, s_1) → P_4
  347. Translate(J'_1, s_1) → Q_4
  348. Translate(I'''_1, s_1) → R_4
  349. Polygon(P_4, Q_4, R_4) → veelhoek23, r_4, p_4, q_4
  350. Translate(M', s_1) → M''_1
  351. Translate(N', s_1) → N''
  352. Translate(O', s_1) → O''
  353. Polygon(M''_1, N'', O'') → veelhoek4'', o'', m''_1, n''
  354. Translate(P', s_1) → P''
  355. Translate(Q', s_1) → Q''
  356. Translate(R', s_1) → R''
  357. Polygon(P'', Q'', R'') → veelhoek5'', r'', p'', q''
  358. Translate(F_1, s_1) → S_4
  359. Translate(G_1, s_1) → T_4
  360. Translate(H_1, s_1) → U_4
  361. Polygon(S_4, T_4, U_4) → veelhoek8', u_4, s_4, t_4
  362. Translate(I_1, s_1) → V_4
  363. Translate(J'', s_1) → J'''
  364. Translate(J_1, s_1) → W_4
  365. Polygon(V_4, J''', W_4) → veelhoek9', w_4, v_4, j'''
  366. Translate(veelhoek1'_1, s_1) → veelhoek24
  367. Translate(F'_5, s_1) → Z_4
  368. Translate(G'_3, s_1) → A_5
  369. Translate(A'_9, s_1) → B_5
  370. Polygon(Z_4, A_5, B_5) → veelhoek25, b_5, z_4, a_6
  371. Translate(H'_3, s_1) → C_5
  372. Translate(A'_{10}, s_1) → D_5
  373. Translate(I'_3, s_1) → E_5
  374. Polygon(C_5, D_5, E_5) → veelhoek26, e_5, c_5, d_5
  375. Translate(F''_3, s_1) → F_5
  376. Translate(G''_3, s_1) → G_5
  377. Translate(A''_2, s_1) → H_5
  378. Polygon(F_5, G_5, H_5) → veelhoek27, h_5, f_5, g_5
  379. Translate(H''_3, s_1) → I_5
  380. Translate(U_1, s_1) → J_5
  381. Translate(I''_2, s_1) → K_5
  382. Polygon(I_5, J_5, K_5) → veelhoek28, k_5, i_5, j_5
  383. Translate(V_1, s_1) → L_5
  384. Translate(W_1, s_1) → M_5
  385. Translate(Z_1, s_1) → N_5
  386. Polygon(L_5, M_5, N_5) → veelhoek10', n_5, l_5, m_5
  387. Translate(A_2, s_1) → O_5
  388. Translate(B_2, s_1) → P_5
  389. Translate(C_2, s_1) → Q_5
  390. Polygon(O_5, P_5, Q_5) → veelhoek11', q_5, o_5, p_5
  391. Translate(F'''_2, s_1) → R_5
  392. Translate(G'''_2, s_1) → S_5
  393. Translate(A'''_2, s_1) → T_5
  394. Polygon(R_5, S_5, T_5) → veelhoek29, t_5, r_5, s_5
  395. Translate(H'''_2, s_1) → U_5
  396. Translate(J'_2, s_1) → V_5
  397. Translate(I'''_2, s_1) → W_5
  398. Polygon(U_5, V_5, W_5) → veelhoek30, w_5, u_5, v_5
  399. Translate(M'_1, s_1) → Z_5
  400. Translate(N'_1, s_1) → A_6
  401. Translate(O'_1, s_1) → B_6
  402. Polygon(Z_5, A_6, B_6) → veelhoek31, b_6, z_5, a_7
  403. Translate(P'_1, s_1) → C_6
  404. Translate(Q'_1, s_1) → D_6
  405. Translate(R'_1, s_1) → E_6
  406. Polygon(C_6, D_6, E_6) → veelhoek32, e_6, c_6, d_6
  407. Translate(D_2, s_1) → F_6
  408. Translate(E_2, s_1) → G_6
  409. Translate(F_2, s_1) → H_6
  410. Polygon(F_6, G_6, H_6) → veelhoek12', h_6, f_6, g_6
  411. Translate(G_2, s_1) → I_6
  412. Translate(J''_1, s_1) → J_6
  413. Translate(H_2, s_1) → K_6
  414. Polygon(I_6, J_6, K_6) → veelhoek13', k_6, i_6, j_6
  415. Translate(F'_1, s_1) → L_6
  416. Translate(A'_2, s_1) → M_6
  417. Segment(L_6, M_6) → i_2
  418. Translate(F'_3, s_1) → N_6
  419. Translate(A'_5, s_1) → O_6
  420. Segment(N_6, O_6) → n_2
  421. Translate(A'_6, s_1) → P_6
  422. Translate(B', s_1) → B''_3
  423. Segment(P_6, B''_3) → p_2
  424. Translate(K, s_1) → K'_3
  425. Translate(L, s_1) → L'_3
  426. Segment(K'_3, L'_3) → k'_3
  427. Translate(C', s_1) → C''_2
  428. Translate(D', s_1) → D''_2
  429. Segment(C''_2, D''_2) → c''_2
  430. Translate(B'_1, s_1) → Q_6
  431. Translate(C'_1, s_1) → R_6
  432. Segment(Q_6, R_6) → b''_2
  433. Translate(F''_1, s_1) → S_6
  434. Translate(G''_1, s_1) → T_6
  435. Segment(S_6, T_6) → q_2
  436. Translate(S, s_1) → S'_2
  437. Translate(T, s_1) → T'_2
  438. Segment(S'_2, T'_2) → l'_2
  439. Translate(U, s_1) → U'_2
  440. Translate(B'', s_1) → B'''_2
  441. Segment(U'_2, B'''_2) → s'_2
  442. Translate(K', s_1) → K''_2
  443. Translate(L', s_1) → L''_2
  444. Segment(K''_2, L''_2) → k''_2
  445. Translate(K_1, s_1) → U_6
  446. Translate(L_1, s_1) → V_6
  447. Segment(U_6, V_6) → t'
  448. Translate(M_1, s_1) → W_6
  449. Translate(N_1, s_1) → Z_6
  450. Segment(W_6, Z_6) → r_2
  451. Translate(O_1, s_1) → A_7
  452. Translate(B''_1, s_1) → B_7
  453. Segment(A_7, B_7) → s_2
  454. Translate(K'_1, s_1) → C_7
  455. Translate(L'_1, s_1) → D_7
  456. Segment(C_7, D_7) → t_2
  457. Translate(C'', s_1) → C'''
  458. Translate(D'', s_1) → D'''
  459. Segment(C''', D''') → c'''
  460. Translate(P_1, s_1) → E_7
  461. Translate(Q_1, s_1) → F_7
  462. Segment(E_7, F_7) → b'''
  463. Translate(R_1, s_1) → G_7
  464. Translate(S_1, s_1) → H_7
  465. Segment(G_7, H_7) → b_3
  466. Translate(S', s_1) → S''_1
  467. Translate(T', s_1) → T''
  468. Segment(S''_1, T'') → l''
  469. Translate(U', s_1) → U''
  470. Translate(B''', s_1) → I_7
  471. Segment(U'', I_7) → s''
  472. Translate(K'', s_1) → K'''
  473. Translate(L'', s_1) → L'''
  474. Segment(K''', L''') → k'''
  475. Translate(L_2, s_1) → J_7
  476. Translate(M_2, s_1) → K_7
  477. Segment(J_7, K_7) → c_3
  478. Translate(N_2, s_1) → L_7
  479. Translate(O_2, s_1) → M_7
  480. Segment(L_7, M_7) → d_3
  481. Translate(P_2, s_1) → N_7
  482. Translate(B''_2, s_1) → O_7
  483. Segment(N_7, O_7) → e_3
  484. Translate(K'_2, s_1) → P_7
  485. Translate(L'_2, s_1) → Q_7
  486. Segment(P_7, Q_7) → i_3
  487. Translate(C''_1, s_1) → R_7
  488. Translate(D''_1, s_1) → S_7
  489. Segment(R_7, S_7) → j_3
  490. Translate(Q_2, s_1) → T_7
  491. Translate(R_2, s_1) → U_7
  492. Segment(T_7, U_7) → l_6
  493. Translate(S_2, s_1) → V_7
  494. Translate(T_2, s_1) → W_7
  495. Segment(V_7, W_7) → m_6
  496. Translate(S'_1, s_1) → Z_7
  497. Translate(T'_1, s_1) → A_8
  498. Segment(Z_7, A_8) → n_6
  499. Translate(U'_1, s_1) → B_8
  500. Translate(B'''_1, s_1) → C_8
  501. Segment(B_8, C_8) → p_6
  502. Translate(K''_1, s_1) → D_8
  503. Translate(L''_1, s_1) → E_8
  504. Segment(D_8, E_8) → q_6
  505. Translate(W_2, s_1) → F_8
  506. Translate(Z_2, s_1) → G_8
  507. Segment(F_8, G_8) → r_6
  508. Translate(A_3, s_1) → H_8
  509. Translate(B_3, s_1) → I_8
  510. Segment(H_8, I_8) → s_6
  511. Translate(C_3, s_1) → J_8
  512. Translate(D_3, s_1) → K_8
  513. Segment(J_8, K_8) → t_6
  514. Translate(H''_1, s_1) → L_8
  515. Translate(V, s_1) → V'_2
  516. Translate(T_1, s_1) → M_8
  517. Translate(V', s_1) → V''_1
  518. Translate(I_2, s_1) → N_8
  519. Translate(J_2, s_1) → O_8
  520. Translate(U_2, s_1) → P_8
  521. Translate(E_3, s_1) → Q_8
  522. Translate(V'_1, s_1) → R_8
  523. Translate(F_3, s_1) → S_8
  524. Translate(M'', s_1) → M'''
  525. Translate(G_3, s_1) → T_8
  526. Translate(H_3, s_1) → U_8
  527. Translate(I_3, s_1) → V_8
  528. Translate(S'', s_1) → S'''
  529. Translate(J_3, s_1) → W_8
  530. Translate(V'', s_1) → V'''
  531. Vector(O'_1, A'_{11}) → u_2
  532. Translate(veelhoek1, u_2) → veelhoek1'_3
  533. Translate(F, u_2) → F'_7
  534. Translate(G, u_2) → G'_5
  535. Translate(A, u_2) → A'_{13}
  536. Polygon(F'_7, G'_5, A'_{13}) → veelhoek2'_5, a'_{13}, f'_7, g'_5
  537. Translate(H, u_2) → H'_5
  538. Translate(A, u_2) → A'_{14}
  539. Translate(I, u_2) → I'_5
  540. Polygon(H'_5, A'_{14}, I'_5) → veelhoek3'_5, i'_5, h'_5, a'_{14}
  541. Translate(F', u_2) → F''_5
  542. Translate(G', u_2) → G''_5
  543. Translate(A', u_2) → A''_4
  544. Polygon(F''_5, G''_5, A''_4) → veelhoek2''_4, a''_5, f''_5, g''_5
  545. Translate(H', u_2) → H''_5
  546. Translate(A'_1, u_2) → Z_8
  547. Translate(I', u_2) → I''_4
  548. Polygon(H''_5, Z_8, I''_4) → veelhoek3''_4, i''_4, h''_5, z_8
  549. Translate(F'_2, u_2) → A_9
  550. Translate(G'_1, u_2) → B_9
  551. Translate(A'_3, u_2) → C_9
  552. Polygon(A_9, B_9, C_9) → veelhoek33, c_9, a_9, b_9
  553. Translate(H'_1, u_2) → D_9
  554. Translate(A'_4, u_2) → E_9
  555. Translate(I'_1, u_2) → F_9
  556. Polygon(D_9, E_9, F_9) → veelhoek34, f_9, d_9, e_9
  557. Translate(F'', u_2) → F'''_4
  558. Translate(G'', u_2) → G'''_4
  559. Translate(A'', u_2) → A'''_4
  560. Polygon(F'''_4, G'''_4, A'''_4) → veelhoek2'''_4, a'''_4, f'''_4, g'''_4
  561. Translate(H'', u_2) → H'''_4
  562. Translate(J, u_2) → J'_4
  563. Translate(I'', u_2) → I'''_4
  564. Polygon(H'''_4, J'_4, I'''_4) → veelhoek3'''_4, i'''_4, h'''_4, j'_4
  565. Translate(M, u_2) → M'_3
  566. Translate(N, u_2) → N'_3
  567. Translate(O, u_2) → O'_3
  568. Polygon(M'_3, N'_3, O'_3) → veelhoek4'_3, o'_3, m'_3, n'_3
  569. Translate(P, u_2) → P'_3
  570. Translate(Q, u_2) → Q'_3
  571. Translate(R, u_2) → R'_3
  572. Polygon(P'_3, Q'_3, R'_3) → veelhoek5'_3, r'_3, p'_3, q'_3
  573. Translate(F''', u_2) → G_9
  574. Translate(G''', u_2) → H_9
  575. Translate(A''', u_2) → I_9
  576. Polygon(G_9, H_9, I_9) → veelhoek35, i_9, g_9, h_9
  577. Translate(H''', u_2) → J_9
  578. Translate(J', u_2) → J''_3
  579. Translate(I''', u_2) → K_9
  580. Polygon(J_9, J''_3, K_9) → veelhoek36, k_9, j_9, j''_3
  581. Translate(veelhoek1', u_2) → veelhoek1''_1
  582. Translate(F'_4, u_2) → L_9
  583. Translate(G'_2, u_2) → M_9
  584. Translate(A'_7, u_2) → N_9
  585. Polygon(L_9, M_9, N_9) → veelhoek37, n_9, l_9, m_9
  586. Translate(H'_2, u_2) → O_9
  587. Translate(A'_8, u_2) → P_9
  588. Translate(I'_2, u_2) → Q_9
  589. Polygon(O_9, P_9, Q_9) → veelhoek38, q_9, o_9, p_9
  590. Translate(F''_2, u_2) → R_9
  591. Translate(G''_2, u_2) → S_9
  592. Translate(A''_1, u_2) → T_9
  593. Polygon(R_9, S_9, T_9) → veelhoek39, t_9, r_9, s_9
  594. Translate(H''_2, u_2) → U_9
  595. Translate(W, u_2) → W'_1
  596. Translate(I''_1, u_2) → V_9
  597. Polygon(U_9, W'_1, V_9) → veelhoek40, v_9, u_9, w'_1
  598. Translate(Z, u_2) → Z'_1
  599. Translate(A_1, u_2) → W_9
  600. Translate(B_1, u_2) → Z_9
  601. Polygon(Z'_1, W_9, Z_9) → veelhoek6'_1, z_9, z'_1, w_9
  602. Translate(C_1, u_2) → A_{10}
  603. Translate(D_1, u_2) → B_{10}
  604. Translate(E_1, u_2) → C_{10}
  605. Polygon(A_{10}, B_{10}, C_{10}) → veelhoek7'_1, c_{10}, a_{10}, b_{10}
  606. Translate(F'''_1, u_2) → D_{10}
  607. Translate(G'''_1, u_2) → E_{10}
  608. Translate(A'''_1, u_2) → F_{10}
  609. Polygon(D_{10}, E_{10}, F_{10}) → veelhoek41, f_{10}, d_{10}, e_{10}
  610. Translate(H'''_1, u_2) → G_{10}
  611. Translate(J'_1, u_2) → H_{10}
  612. Translate(I'''_1, u_2) → I_{10}
  613. Polygon(G_{10}, H_{10}, I_{10}) → veelhoek42, i_{10}, g_{10}, h_{10}
  614. Translate(M', u_2) → M''_2
  615. Translate(N', u_2) → N''_1
  616. Translate(O', u_2) → O''_1
  617. Polygon(M''_2, N''_1, O''_1) → veelhoek4''_1, o''_1, m''_2, n''_1
  618. Translate(P', u_2) → P''_1
  619. Translate(Q', u_2) → Q''_1
  620. Translate(R', u_2) → R''_1
  621. Polygon(P''_1, Q''_1, R''_1) → veelhoek5''_1, r''_1, p''_1, q''_1
  622. Translate(F_1, u_2) → J_{10}
  623. Translate(G_1, u_2) → K_{10}
  624. Translate(H_1, u_2) → L_{10}
  625. Polygon(J_{10}, K_{10}, L_{10}) → veelhoek8'_1, l_{10}, j_{10}, k_{10}
  626. Translate(I_1, u_2) → M_{10}
  627. Translate(J'', u_2) → J'''_1
  628. Translate(J_1, u_2) → N_{10}
  629. Polygon(M_{10}, J'''_1, N_{10}) → veelhoek9'_1, n_{10}, m_{10}, j'''_1
  630. Translate(veelhoek1'_1, u_2) → veelhoek43
  631. Translate(F'_5, u_2) → O_{10}
  632. Translate(G'_3, u_2) → P_{10}
  633. Translate(A'_9, u_2) → Q_{10}
  634. Polygon(O_{10}, P_{10}, Q_{10}) → veelhoek44, q_{10}, o_{10}, p_{10}
  635. Translate(H'_3, u_2) → R_{10}
  636. Translate(A'_{10}, u_2) → S_{10}
  637. Translate(I'_3, u_2) → T_{10}
  638. Polygon(R_{10}, S_{10}, T_{10}) → veelhoek45, t_{10}, r_{10}, s_{10}
  639. Translate(F''_3, u_2) → U_{10}
  640. Translate(G''_3, u_2) → V_{10}
  641. Translate(A''_2, u_2) → W_{10}
  642. Polygon(U_{10}, V_{10}, W_{10}) → veelhoek46, w_{10}, u_{10}, v_{10}
  643. Translate(H''_3, u_2) → Z_{10}
  644. Translate(U_1, u_2) → A_{11}
  645. Translate(I''_2, u_2) → B_{11}
  646. Polygon(Z_{10}, A_{11}, B_{11}) → veelhoek47, b_{11}, z_{10}, a_{11}
  647. Translate(V_1, u_2) → C_{11}
  648. Translate(W_1, u_2) → D_{11}
  649. Translate(Z_1, u_2) → E_{11}
  650. Polygon(C_{11}, D_{11}, E_{11}) → veelhoek10'_1, e_{11}, c_{11}, d_{11}
  651. Translate(A_2, u_2) → F_{11}
  652. Translate(B_2, u_2) → G_{11}
  653. Translate(C_2, u_2) → H_{11}
  654. Polygon(F_{11}, G_{11}, H_{11}) → veelhoek11'_1, h_{11}, f_{11}, g_{11}
  655. Translate(F'''_2, u_2) → I_{11}
  656. Translate(G'''_2, u_2) → J_{11}
  657. Translate(A'''_2, u_2) → K_{11}
  658. Polygon(I_{11}, J_{11}, K_{11}) → veelhoek48, k_{11}, i_{11}, j_{11}
  659. Translate(H'''_2, u_2) → L_{11}
  660. Translate(J'_2, u_2) → M_{11}
  661. Translate(I'''_2, u_2) → N_{11}
  662. Polygon(L_{11}, M_{11}, N_{11}) → veelhoek49, n_{11}, l_{11}, m_{11}
  663. Translate(M'_1, u_2) → O_{11}
  664. Translate(N'_1, u_2) → P_{11}
  665. Translate(O'_1, u_2) → Q_{11}
  666. Polygon(O_{11}, P_{11}, Q_{11}) → veelhoek50, q_{11}, o_{11}, p_{11}
  667. Translate(P'_1, u_2) → R_{11}
  668. Translate(Q'_1, u_2) → S_{11}
  669. Translate(R'_1, u_2) → T_{11}
  670. Polygon(R_{11}, S_{11}, T_{11}) → veelhoek51, t_{11}, r_{11}, s_{11}
  671. Translate(D_2, u_2) → U_{11}
  672. Translate(E_2, u_2) → V_{11}
  673. Translate(F_2, u_2) → W_{11}
  674. Polygon(U_{11}, V_{11}, W_{11}) → veelhoek12'_1, w_{11}, u_{11}, v_{11}
  675. Translate(G_2, u_2) → Z_{11}
  676. Translate(J''_1, u_2) → A_{12}
  677. Translate(H_2, u_2) → B_{12}
  678. Polygon(Z_{11}, A_{12}, B_{12}) → veelhoek13'_1, b_{12}, z_{11}, a_{12}
  679. Translate(veelhoek1'_2, u_2) → veelhoek52
  680. Translate(F'_6, u_2) → C_{12}
  681. Translate(G'_4, u_2) → D_{12}
  682. Translate(A'_{11}, u_2) → E_{12}
  683. Polygon(C_{12}, D_{12}, E_{12}) → veelhoek53, e_{12}, c_{12}, d_{12}
  684. Translate(H'_4, u_2) → F_{12}
  685. Translate(A'_{12}, u_2) → G_{12}
  686. Translate(I'_4, u_2) → H_{12}
  687. Polygon(F_{12}, G_{12}, H_{12}) → veelhoek54, h_{12}, f_{12}, g_{12}
  688. Translate(F''_4, u_2) → I_{12}
  689. Translate(G''_4, u_2) → J_{12}
  690. Translate(A''_3, u_2) → K_{12}
  691. Polygon(I_{12}, J_{12}, K_{12}) → veelhoek55, k_{12}, i_{12}, j_{12}
  692. Translate(H''_4, u_2) → L_{12}
  693. Translate(K_2, u_2) → M_{12}
  694. Translate(I''_3, u_2) → N_{12}
  695. Polygon(L_{12}, M_{12}, N_{12}) → veelhoek56, n_{12}, l_{12}, m_{12}
  696. Translate(V_2, u_2) → O_{12}
  697. Translate(K_3, u_2) → P_{12}
  698. Translate(L_3, u_2) → Q_{12}
  699. Polygon(O_{12}, P_{12}, Q_{12}) → veelhoek14', q_{12}, o_{12}, p_{12}
  700. Translate(M_3, u_2) → R_{12}
  701. Translate(N_3, u_2) → S_{12}
  702. Translate(O_3, u_2) → T_{12}
  703. Polygon(R_{12}, S_{12}, T_{12}) → veelhoek15', t_{12}, r_{12}, s_{12}
  704. Translate(F'''_3, u_2) → U_{12}
  705. Translate(G'''_3, u_2) → V_{12}
  706. Translate(A'''_3, u_2) → W_{12}
  707. Polygon(U_{12}, V_{12}, W_{12}) → veelhoek57, w_{12}, u_{12}, v_{12}
  708. Translate(H'''_3, u_2) → Z_{12}
  709. Translate(J'_3, u_2) → A_{13}
  710. Translate(I'''_3, u_2) → B_{13}
  711. Polygon(Z_{12}, A_{13}, B_{13}) → veelhoek58, b_{13}, z_{12}, a_{13}
  712. Translate(M'_2, u_2) → C_{13}
  713. Translate(N'_2, u_2) → D_{13}
  714. Translate(O'_2, u_2) → E_{13}
  715. Polygon(C_{13}, D_{13}, E_{13}) → veelhoek59, e_{13}, c_{13}, d_{13}
  716. Translate(P'_2, u_2) → F_{13}
  717. Translate(Q'_2, u_2) → G_{13}
  718. Translate(R'_2, u_2) → H_{13}
  719. Polygon(F_{13}, G_{13}, H_{13}) → veelhoek60, h_{13}, f_{13}, g_{13}
  720. Translate(P_3, u_2) → I_{13}
  721. Translate(Q_3, u_2) → J_{13}
  722. Translate(R_3, u_2) → K_{13}
  723. Polygon(I_{13}, J_{13}, K_{13}) → veelhoek16', k_{13}, i_{13}, j_{13}
  724. Translate(S_3, u_2) → L_{13}
  725. Translate(J''_2, u_2) → M_{13}
  726. Translate(T_3, u_2) → N_{13}
  727. Polygon(L_{13}, M_{13}, N_{13}) → veelhoek17', n_{13}, l_{13}, m_{13}
  728. Translate(veelhoek1'', u_2) → veelhoek1'''
  729. Translate(U_3, u_2) → O_{13}
  730. Translate(V_3, u_2) → P_{13}
  731. Translate(W_3, u_2) → Q_{13}
  732. Polygon(O_{13}, P_{13}, Q_{13}) → veelhoek18', q_{13}, o_{13}, p_{13}
  733. Translate(Z_3, u_2) → R_{13}
  734. Translate(A_4, u_2) → S_{13}
  735. Translate(B_4, u_2) → T_{13}
  736. Polygon(R_{13}, S_{13}, T_{13}) → veelhoek19', t_{13}, r_{13}, s_{13}
  737. Translate(C_4, u_2) → U_{13}
  738. Translate(D_4, u_2) → V_{13}
  739. Translate(E_4, u_2) → W_{13}
  740. Polygon(U_{13}, V_{13}, W_{13}) → veelhoek20', w_{13}, u_{13}, v_{13}
  741. Translate(F_4, u_2) → Z_{13}
  742. Translate(W', u_2) → W''
  743. Translate(G_4, u_2) → A_{14}
  744. Polygon(Z_{13}, W'', A_{14}) → veelhoek21', a_{14}, z_{13}, w''
  745. Translate(Z', u_2) → Z''
  746. Translate(H_4, u_2) → B_{14}
  747. Translate(I_4, u_2) → C_{14}
  748. Polygon(Z'', B_{14}, C_{14}) → veelhoek6'', c_{14}, z'', b_{14}
  749. Translate(J_4, u_2) → D_{14}
  750. Translate(K_4, u_2) → E_{14}
  751. Translate(L_4, u_2) → F_{14}
  752. Polygon(D_{14}, E_{14}, F_{14}) → veelhoek7'', f_{14}, d_{14}, e_{14}
  753. Translate(M_4, u_2) → G_{14}
  754. Translate(N_4, u_2) → H_{14}
  755. Translate(O_4, u_2) → I_{14}
  756. Polygon(G_{14}, H_{14}, I_{14}) → veelhoek22', i_{14}, g_{14}, h_{14}
  757. Translate(P_4, u_2) → J_{14}
  758. Translate(Q_4, u_2) → K_{14}
  759. Translate(R_4, u_2) → L_{14}
  760. Polygon(J_{14}, K_{14}, L_{14}) → veelhoek23', l_{14}, j_{14}, k_{14}
  761. Translate(M''_1, u_2) → M_{14}
  762. Translate(N'', u_2) → N'''
  763. Translate(O'', u_2) → O'''
  764. Polygon(M_{14}, N''', O''') → veelhoek4''', o''', m_{14}, n'''
  765. Translate(P'', u_2) → P'''
  766. Translate(Q'', u_2) → Q'''
  767. Translate(R'', u_2) → R'''
  768. Polygon(P''', Q''', R''') → veelhoek5''', r''', p''', q'''
  769. Translate(S_4, u_2) → N_{14}
  770. Translate(T_4, u_2) → O_{14}
  771. Translate(U_4, u_2) → P_{14}
  772. Polygon(N_{14}, O_{14}, P_{14}) → veelhoek8'', p_{14}, n_{14}, o_{14}
  773. Translate(V_4, u_2) → Q_{14}
  774. Translate(J''', u_2) → R_{14}
  775. Translate(W_4, u_2) → S_{14}
  776. Polygon(Q_{14}, R_{14}, S_{14}) → veelhoek9'', s_{14}, q_{14}, r_{14}
  777. Translate(veelhoek24, u_2) → veelhoek24'
  778. Translate(Z_4, u_2) → T_{14}
  779. Translate(A_5, u_2) → U_{14}
  780. Translate(B_5, u_2) → V_{14}
  781. Polygon(T_{14}, U_{14}, V_{14}) → veelhoek25', v_{14}, t_{14}, u_{14}
  782. Translate(C_5, u_2) → W_{14}
  783. Translate(D_5, u_2) → Z_{14}
  784. Translate(E_5, u_2) → A_{15}
  785. Polygon(W_{14}, Z_{14}, A_{15}) → veelhoek26', a_{15}, w_{14}, z_{14}
  786. Translate(F_5, u_2) → B_{15}
  787. Translate(G_5, u_2) → C_{15}
  788. Translate(H_5, u_2) → D_{15}
  789. Polygon(B_{15}, C_{15}, D_{15}) → veelhoek27', d_{15}, b_{15}, c_{15}
  790. Translate(I_5, u_2) → E_{15}
  791. Translate(J_5, u_2) → F_{15}
  792. Translate(K_5, u_2) → G_{15}
  793. Polygon(E_{15}, F_{15}, G_{15}) → veelhoek28', g_{15}, e_{15}, f_{15}
  794. Translate(L_5, u_2) → H_{15}
  795. Translate(M_5, u_2) → I_{15}
  796. Translate(N_5, u_2) → J_{15}
  797. Polygon(H_{15}, I_{15}, J_{15}) → veelhoek10'', j_{15}, h_{15}, i_{15}
  798. Translate(O_5, u_2) → K_{15}
  799. Translate(P_5, u_2) → L_{15}
  800. Translate(Q_5, u_2) → M_{15}
  801. Polygon(K_{15}, L_{15}, M_{15}) → veelhoek11'', m_{15}, k_{15}, l_{15}
  802. Translate(R_5, u_2) → N_{15}
  803. Translate(S_5, u_2) → O_{15}
  804. Translate(T_5, u_2) → P_{15}
  805. Polygon(N_{15}, O_{15}, P_{15}) → veelhoek29', p_{15}, n_{15}, o_{15}
  806. Translate(U_5, u_2) → Q_{15}
  807. Translate(V_5, u_2) → R_{15}
  808. Translate(W_5, u_2) → S_{15}
  809. Polygon(Q_{15}, R_{15}, S_{15}) → veelhoek30', s_{15}, q_{15}, r_{15}
  810. Translate(Z_5, u_2) → T_{15}
  811. Translate(A_6, u_2) → U_{15}
  812. Translate(B_6, u_2) → V_{15}
  813. Polygon(T_{15}, U_{15}, V_{15}) → veelhoek31', v_{15}, t_{15}, u_{15}
  814. Translate(C_6, u_2) → W_{15}
  815. Translate(D_6, u_2) → Z_{15}
  816. Translate(E_6, u_2) → A_{16}
  817. Polygon(W_{15}, Z_{15}, A_{16}) → veelhoek32', a_{16}, w_{15}, z_{15}
  818. Translate(F_6, u_2) → B_{16}
  819. Translate(G_6, u_2) → C_{16}
  820. Translate(H_6, u_2) → D_{16}
  821. Polygon(B_{16}, C_{16}, D_{16}) → veelhoek12'', d_{16}, b_{16}, c_{16}
  822. Translate(I_6, u_2) → E_{16}
  823. Translate(J_6, u_2) → F_{16}
  824. Translate(K_6, u_2) → G_{16}
  825. Polygon(E_{16}, F_{16}, G_{16}) → veelhoek13'', g_{16}, e_{16}, f_{16}
  826. Translate(F'_1, u_2) → H_{16}
  827. Translate(A'_2, u_2) → I_{16}
  828. Segment(H_{16}, I_{16}) → b_7
  829. Translate(F'_3, u_2) → J_{16}
  830. Translate(A'_5, u_2) → K_{16}
  831. Segment(J_{16}, K_{16}) → c_7
  832. Translate(A'_6, u_2) → L_{16}
  833. Translate(B', u_2) → B''_4
  834. Segment(L_{16}, B''_4) → d_7
  835. Translate(K, u_2) → K'_4
  836. Translate(L, u_2) → L'_4
  837. Segment(K'_4, L'_4) → k'_4
  838. Translate(C', u_2) → C''_3
  839. Translate(D', u_2) → D''_3
  840. Segment(C''_3, D''_3) → c''_3
  841. Translate(B'_1, u_2) → M_{16}
  842. Translate(C'_1, u_2) → N_{16}
  843. Segment(M_{16}, N_{16}) → b''_3
  844. Translate(F''_1, u_2) → O_{16}
  845. Translate(G''_1, u_2) → P_{16}
  846. Segment(O_{16}, P_{16}) → e_7
  847. Translate(S, u_2) → S'_3
  848. Translate(T, u_2) → T'_3
  849. Segment(S'_3, T'_3) → l'_3
  850. Translate(U, u_2) → U'_3
  851. Translate(B'', u_2) → B'''_3
  852. Segment(U'_3, B'''_3) → s'_3
  853. Translate(K', u_2) → K''_3
  854. Translate(L', u_2) → L''_3
  855. Segment(K''_3, L''_3) → k''_3
  856. Translate(K_1, u_2) → Q_{16}
  857. Translate(L_1, u_2) → R_{16}
  858. Segment(Q_{16}, R_{16}) → t'_1
  859. Translate(M_1, u_2) → S_{16}
  860. Translate(N_1, u_2) → T_{16}
  861. Segment(S_{16}, T_{16}) → f_7
  862. Translate(O_1, u_2) → U_{16}
  863. Translate(B''_1, u_2) → V_{16}
  864. Segment(U_{16}, V_{16}) → g_7
  865. Translate(K'_1, u_2) → W_{16}
  866. Translate(L'_1, u_2) → Z_{16}
  867. Segment(W_{16}, Z_{16}) → h_7
  868. Translate(C'', u_2) → C'''_1
  869. Translate(D'', u_2) → D'''_1
  870. Segment(C'''_1, D'''_1) → c'''_1
  871. Translate(P_1, u_2) → A_{17}
  872. Translate(Q_1, u_2) → B_{17}
  873. Segment(A_{17}, B_{17}) → b'''_1
  874. Translate(R_1, u_2) → C_{17}
  875. Translate(S_1, u_2) → D_{17}
  876. Segment(C_{17}, D_{17}) → i_7
  877. Translate(S', u_2) → S''_2
  878. Translate(T', u_2) → T''_1
  879. Segment(S''_2, T''_1) → l''_1
  880. Translate(U', u_2) → U''_1
  881. Translate(B''', u_2) → E_{17}
  882. Segment(U''_1, E_{17}) → s''_1
  883. Translate(K'', u_2) → K'''_1
  884. Translate(L'', u_2) → L'''_1
  885. Segment(K'''_1, L'''_1) → k'''_1
  886. Translate(L_2, u_2) → F_{17}
  887. Translate(M_2, u_2) → G_{17}
  888. Segment(F_{17}, G_{17}) → j_7
  889. Translate(N_2, u_2) → H_{17}
  890. Translate(O_2, u_2) → I_{17}
  891. Segment(H_{17}, I_{17}) → k_7
  892. Translate(P_2, u_2) → J_{17}
  893. Translate(B''_2, u_2) → K_{17}
  894. Segment(J_{17}, K_{17}) → l_7
  895. Translate(K'_2, u_2) → L_{17}
  896. Translate(L'_2, u_2) → M_{17}
  897. Segment(L_{17}, M_{17}) → m_7
  898. Translate(C''_1, u_2) → N_{17}
  899. Translate(D''_1, u_2) → O_{17}
  900. Segment(N_{17}, O_{17}) → n_7
  901. Translate(Q_2, u_2) → P_{17}
  902. Translate(R_2, u_2) → Q_{17}
  903. Segment(P_{17}, Q_{17}) → p_7
  904. Translate(S_2, u_2) → R_{17}
  905. Translate(T_2, u_2) → S_{17}
  906. Segment(R_{17}, S_{17}) → q_7
  907. Translate(S'_1, u_2) → T_{17}
  908. Translate(T'_1, u_2) → U_{17}
  909. Segment(T_{17}, U_{17}) → r_7
  910. Translate(U'_1, u_2) → V_{17}
  911. Translate(B'''_1, u_2) → W_{17}
  912. Segment(V_{17}, W_{17}) → s_7
  913. Translate(K''_1, u_2) → Z_{17}
  914. Translate(L''_1, u_2) → A_{18}
  915. Segment(Z_{17}, A_{18}) → t_7
  916. Translate(W_2, u_2) → B_{18}
  917. Translate(Z_2, u_2) → C_{18}
  918. Segment(B_{18}, C_{18}) → a_8
  919. Translate(A_3, u_2) → D_{18}
  920. Translate(B_3, u_2) → E_{18}
  921. Segment(D_{18}, E_{18}) → b_8
  922. Translate(C_3, u_2) → F_{18}
  923. Translate(D_3, u_2) → G_{18}
  924. Segment(F_{18}, G_{18}) → c_8
  925. Translate(L_6, u_2) → H_{18}
  926. Translate(M_6, u_2) → I_{18}
  927. Segment(H_{18}, I_{18}) → d_8
  928. Translate(N_6, u_2) → J_{18}
  929. Translate(O_6, u_2) → K_{18}
  930. Segment(J_{18}, K_{18}) → e_8
  931. Translate(P_6, u_2) → L_{18}
  932. Translate(B''_3, u_2) → M_{18}
  933. Segment(L_{18}, M_{18}) → f_8
  934. Translate(K'_3, u_2) → N_{18}
  935. Translate(L'_3, u_2) → O_{18}
  936. Segment(N_{18}, O_{18}) → g_8
  937. Translate(C''_2, u_2) → P_{18}
  938. Translate(D''_2, u_2) → Q_{18}
  939. Segment(P_{18}, Q_{18}) → h_8
  940. Translate(Q_6, u_2) → R_{18}
  941. Translate(R_6, u_2) → S_{18}
  942. Segment(R_{18}, S_{18}) → i_8
  943. Translate(S_6, u_2) → T_{18}
  944. Translate(T_6, u_2) → U_{18}
  945. Segment(T_{18}, U_{18}) → j_8
  946. Translate(S'_2, u_2) → V_{18}
  947. Translate(T'_2, u_2) → W_{18}
  948. Segment(V_{18}, W_{18}) → k_8
  949. Translate(U'_2, u_2) → Z_{18}
  950. Translate(B'''_2, u_2) → A_{19}
  951. Segment(Z_{18}, A_{19}) → l_8
  952. Translate(K''_2, u_2) → B_{19}
  953. Translate(L''_2, u_2) → C_{19}
  954. Segment(B_{19}, C_{19}) → m_8
  955. Translate(U_6, u_2) → D_{19}
  956. Translate(V_6, u_2) → E_{19}
  957. Segment(D_{19}, E_{19}) → t''
  958. Translate(W_6, u_2) → F_{19}
  959. Translate(Z_6, u_2) → G_{19}
  960. Segment(F_{19}, G_{19}) → n_8
  961. Translate(A_7, u_2) → H_{19}
  962. Translate(B_7, u_2) → I_{19}
  963. Segment(H_{19}, I_{19}) → p_8
  964. Translate(C_7, u_2) → J_{19}
  965. Translate(D_7, u_2) → K_{19}
  966. Segment(J_{19}, K_{19}) → q_8
  967. Translate(C''', u_2) → L_{19}
  968. Translate(D''', u_2) → M_{19}
  969. Segment(L_{19}, M_{19}) → r_8
  970. Translate(E_7, u_2) → N_{19}
  971. Translate(F_7, u_2) → O_{19}
  972. Segment(N_{19}, O_{19}) → s_8
  973. Translate(G_7, u_2) → P_{19}
  974. Translate(H_7, u_2) → Q_{19}
  975. Segment(P_{19}, Q_{19}) → t_8
  976. Translate(S''_1, u_2) → R_{19}
  977. Translate(T'', u_2) → T'''
  978. Segment(R_{19}, T''') → l'''
  979. Translate(U'', u_2) → U'''
  980. Translate(I_7, u_2) → S_{19}
  981. Segment(U''', S_{19}) → s'''
  982. Translate(K''', u_2) → T_{19}
  983. Translate(L''', u_2) → U_{19}
  984. Segment(T_{19}, U_{19}) → h_{16}
  985. Translate(J_7, u_2) → V_{19}
  986. Translate(K_7, u_2) → W_{19}
  987. Segment(V_{19}, W_{19}) → i_{16}
  988. Translate(L_7, u_2) → Z_{19}
  989. Translate(M_7, u_2) → A_{20}
  990. Segment(Z_{19}, A_{20}) → j_{16}
  991. Translate(N_7, u_2) → B_{20}
  992. Translate(O_7, u_2) → C_{20}
  993. Segment(B_{20}, C_{20}) → k_{16}
  994. Translate(P_7, u_2) → D_{20}
  995. Translate(Q_7, u_2) → E_{20}
  996. Segment(D_{20}, E_{20}) → l_{16}
  997. Translate(R_7, u_2) → F_{20}
  998. Translate(S_7, u_2) → G_{20}
  999. Segment(F_{20}, G_{20}) → m_{16}
  1000. Translate(T_7, u_2) → H_{20}
  1001. Translate(U_7, u_2) → I_{20}
  1002. Segment(H_{20}, I_{20}) → n_{16}
  1003. Translate(V_7, u_2) → J_{20}
  1004. Translate(W_7, u_2) → K_{20}
  1005. Segment(J_{20}, K_{20}) → p_{16}
  1006. Translate(Z_7, u_2) → L_{20}
  1007. Translate(A_8, u_2) → M_{20}
  1008. Segment(L_{20}, M_{20}) → q_{16}
  1009. Translate(B_8, u_2) → N_{20}
  1010. Translate(C_8, u_2) → O_{20}
  1011. Segment(N_{20}, O_{20}) → r_{16}
  1012. Translate(D_8, u_2) → P_{20}
  1013. Translate(E_8, u_2) → Q_{20}
  1014. Segment(P_{20}, Q_{20}) → s_{16}
  1015. Translate(F_8, u_2) → R_{20}
  1016. Translate(G_8, u_2) → S_{20}
  1017. Segment(R_{20}, S_{20}) → t_{16}
  1018. Translate(H_8, u_2) → T_{20}
  1019. Translate(I_8, u_2) → U_{20}
  1020. Segment(T_{20}, U_{20}) → a_{17}
  1021. Translate(J_8, u_2) → V_{20}
  1022. Translate(K_8, u_2) → W_{20}
  1023. Segment(V_{20}, W_{20}) → b_{17}
  1024. Translate(H''_1, u_2) → Z_{20}
  1025. Translate(V, u_2) → V'_3
  1026. Translate(T_1, u_2) → A_{21}
  1027. Translate(V', u_2) → V''_2
  1028. Translate(I_2, u_2) → B_{21}
  1029. Translate(J_2, u_2) → C_{21}
  1030. Translate(U_2, u_2) → D_{21}
  1031. Translate(E_3, u_2) → E_{21}
  1032. Translate(V'_1, u_2) → F_{21}
  1033. Translate(F_3, u_2) → G_{21}
  1034. Translate(M'', u_2) → M'''_1
  1035. Translate(G_3, u_2) → H_{21}
  1036. Translate(H_3, u_2) → I_{21}
  1037. Translate(I_3, u_2) → J_{21}
  1038. Translate(S'', u_2) → S'''_1
  1039. Translate(J_3, u_2) → K_{21}
  1040. Translate(V'', u_2) → V'''_1
  1041. Translate(L_8, u_2) → L_{21}
  1042. Translate(V'_2, u_2) → M_{21}
  1043. Translate(M_8, u_2) → N_{21}
  1044. Translate(V''_1, u_2) → O_{21}
  1045. Translate(N_8, u_2) → P_{21}
  1046. Translate(O_8, u_2) → Q_{21}
  1047. Translate(P_8, u_2) → R_{21}
  1048. Translate(Q_8, u_2) → S_{21}
  1049. Translate(R_8, u_2) → T_{21}
  1050. Translate(S_8, u_2) → U_{21}
  1051. Translate(M''', u_2) → V_{21}
  1052. Translate(T_8, u_2) → W_{21}
  1053. Translate(U_8, u_2) → Z_{21}
  1054. Translate(V_8, u_2) → A_{22}
  1055. Translate(S''', u_2) → B_{22}
  1056. Translate(W_8, u_2) → C_{22}
  1057. Translate(V''', u_2) → D_{22}
  1058. Line(D, F) → c_{17}
  1059. Line(B, F) → d_{17}
  1060. Line(F'''_2, F'_5) → e_{17}
  1061. Line(F'_6, F'_4) → f_{17}
  1062. Vector(C, O'') → w_2
  1063. Translate(veelhoek1, w_2) → veelhoek1'_4
  1064. Translate(F, w_2) → F'_8
  1065. Translate(G, w_2) → G'_6
  1066. Translate(A, w_2) → A'_{15}
  1067. Polygon(F'_8, G'_6, A'_{15}) → veelhoek2'_6, a'_{15}, f'_8, g'_6
  1068. Translate(H, w_2) → H'_6
  1069. Translate(A, w_2) → A'_{16}
  1070. Translate(I, w_2) → I'_6
  1071. Polygon(H'_6, A'_{16}, I'_6) → veelhoek3'_6, i'_6, h'_6, a'_{16}
  1072. Translate(F', w_2) → F''_6
  1073. Translate(G', w_2) → G''_6
  1074. Translate(A', w_2) → A''_5
  1075. Polygon(F''_6, G''_6, A''_5) → veelhoek2''_5, a''_6, f''_6, g''_6
  1076. Translate(H', w_2) → H''_6
  1077. Translate(A'_1, w_2) → E_{22}
  1078. Translate(I', w_2) → I''_5
  1079. Polygon(H''_6, E_{22}, I''_5) → veelhoek3''_5, i''_5, h''_6, e_{22}
  1080. Translate(F'_2, w_2) → F_{22}
  1081. Translate(G'_1, w_2) → G_{22}
  1082. Translate(A'_3, w_2) → H_{22}
  1083. Polygon(F_{22}, G_{22}, H_{22}) → veelhoek61, h_{22}, f_{22}, g_{22}
  1084. Translate(H'_1, w_2) → I_{22}
  1085. Translate(A'_4, w_2) → J_{22}
  1086. Translate(I'_1, w_2) → K_{22}
  1087. Polygon(I_{22}, J_{22}, K_{22}) → veelhoek62, k_{22}, i_{22}, j_{22}
  1088. Translate(F'', w_2) → F'''_5
  1089. Translate(G'', w_2) → G'''_5
  1090. Translate(A'', w_2) → A'''_5
  1091. Polygon(F'''_5, G'''_5, A'''_5) → veelhoek2'''_5, a'''_5, f'''_5, g'''_5
  1092. Translate(H'', w_2) → H'''_5
  1093. Translate(J, w_2) → J'_5
  1094. Translate(I'', w_2) → I'''_5
  1095. Polygon(H'''_5, J'_5, I'''_5) → veelhoek3'''_5, i'''_5, h'''_5, j'_5
  1096. Translate(M, w_2) → M'_4
  1097. Translate(N, w_2) → N'_4
  1098. Translate(O, w_2) → O'_4
  1099. Polygon(M'_4, N'_4, O'_4) → veelhoek4'_4, o'_4, m'_4, n'_4
  1100. Translate(P, w_2) → P'_4
  1101. Translate(Q, w_2) → Q'_4
  1102. Translate(R, w_2) → R'_4
  1103. Polygon(P'_4, Q'_4, R'_4) → veelhoek5'_4, r'_4, p'_4, q'_4
  1104. Translate(F''', w_2) → L_{22}
  1105. Translate(G''', w_2) → M_{22}
  1106. Translate(A''', w_2) → N_{22}
  1107. Polygon(L_{22}, M_{22}, N_{22}) → veelhoek63, n_{22}, l_{22}, m_{22}
  1108. Translate(H''', w_2) → O_{22}
  1109. Translate(J', w_2) → J''_4
  1110. Translate(I''', w_2) → P_{22}
  1111. Polygon(O_{22}, J''_4, P_{22}) → veelhoek64, p_{22}, o_{22}, j''_4
  1112. Translate(H'''_1, w_2) → Q_{22}
  1113. Translate(J'_1, w_2) → R_{22}
  1114. Translate(I'''_1, w_2) → S_{22}
  1115. Polygon(Q_{22}, R_{22}, S_{22}) → veelhoek65, s_{22}, q_{22}, r_{22}
  1116. Translate(A_2, w_2) → T_{22}
  1117. Translate(B_2, w_2) → U_{22}
  1118. Translate(C_2, w_2) → V_{22}
  1119. Polygon(T_{22}, U_{22}, V_{22}) → veelhoek11'_2, v_{22}, t_{22}, u_{22}
  1120. Translate(F'_1, w_2) → W_{22}
  1121. Translate(A'_2, w_2) → Z_{22}
  1122. Segment(W_{22}, Z_{22}) → g_{17}
  1123. Translate(F'_3, w_2) → A_{23}
  1124. Translate(A'_5, w_2) → B_{23}
  1125. Segment(A_{23}, B_{23}) → h_{17}
  1126. Translate(A'_6, w_2) → C_{23}
  1127. Translate(B', w_2) → B''_5
  1128. Segment(C_{23}, B''_5) → i_{17}
  1129. Translate(K, w_2) → K'_5
  1130. Translate(L, w_2) → L'_5
  1131. Segment(K'_5, L'_5) → k'_5
  1132. Translate(C', w_2) → C''_4
  1133. Translate(D', w_2) → D''_4
  1134. Segment(C''_4, D''_4) → c''_4
  1135. Translate(B'_1, w_2) → D_{23}
  1136. Translate(C'_1, w_2) → E_{23}
  1137. Segment(D_{23}, E_{23}) → b''_4
  1138. Translate(F''_1, w_2) → F_{23}
  1139. Translate(G''_1, w_2) → G_{23}
  1140. Segment(F_{23}, G_{23}) → j_{17}
  1141. Translate(S, w_2) → S'_4
  1142. Translate(T, w_2) → T'_4
  1143. Segment(S'_4, T'_4) → l'_4
  1144. Translate(U, w_2) → U'_4
  1145. Translate(B'', w_2) → B'''_4
  1146. Segment(U'_4, B'''_4) → s'_4
  1147. Translate(K', w_2) → K''_4
  1148. Translate(L', w_2) → L''_4
  1149. Segment(K''_4, L''_4) → k''_4
  1150. Translate(D_1, w_2) → H_{23}
  1151. Translate(E_1, w_2) → I_{23}
  1152. Segment(H_{23}, I_{23}) → k_{17}
  1153. Translate(A'''_1, w_2) → J_{23}
  1154. Translate(F'''_1, w_2) → K_{23}
  1155. Segment(J_{23}, K_{23}) → l_{17}
  1156. Translate(O_1, w_2) → L_{23}
  1157. Translate(B''_1, w_2) → M_{23}
  1158. Segment(L_{23}, M_{23}) → m_{17}
  1159. Translate(K'_1, w_2) → N_{23}
  1160. Translate(L'_1, w_2) → O_{23}
  1161. Segment(N_{23}, O_{23}) → n_{17}
  1162. Translate(Z_1, w_2) → P_{23}
  1163. Translate(V_1, w_2) → Q_{23}
  1164. Segment(P_{23}, Q_{23}) → p_{17}
  1165. Translate(J'_2, w_2) → R_{23}
  1166. Translate(I'''_2, w_2) → S_{23}
  1167. Segment(R_{23}, S_{23}) → q_{17}
  1168. Translate(N_2, w_2) → T_{23}
  1169. Translate(O_2, w_2) → U_{23}
  1170. Segment(T_{23}, U_{23}) → r_{17}
  1171. Translate(H''_1, w_2) → V_{23}
  1172. Translate(V, w_2) → V'_4
  1173. Translate(B_1, w_2) → W_{23}
  1174. Translate(M', w_2) → M''_3
  1175. Translate(P', w_2) → P''_2
  1176. Translate(N_1, w_2) → Z_{23}
  1177. Translate(P_1, w_2) → A_{24}
  1178. Translate(R_1, w_2) → B_{24}
  1179. Translate(S', w_2) → S''_3
  1180. Translate(T_1, w_2) → C_{24}
  1181. Translate(V', w_2) → V''_3
  1182. Translate(F''_3, w_2) → D_{24}
  1183. Translate(H''_3, w_2) → E_{24}
  1184. Translate(A'''_2, w_2) → F_{24}
  1185. Translate(L_2, w_2) → G_{24}
  1186. Translate(P_2, w_2) → H_{24}
  1187. Translate(L'_2, w_2) → I_{24}

AI Drawing Prompt Reference

Draw a hexagon, find the perpendicular bisector of one side, then another side's perpendicular bisector, and connect their intersection to a vertex and its opposite vertex to form a triangle. Rotate this triangle by 120 degrees and translate it along one side of the hexagon to create another triangle. Repeat these steps to generate multiple rotated and translated shapes, demonstrating symmetry in periodic tiling.
The prompt above was compiled from the original drawing commands and is for reference only.