MathPlotAI Logo MathPlotAI

Step Seven: Create a Tessellation

Step Seven: Create a Tessellation
Loading the math board and drawing, please wait…
2014-03-29 05:39
VectorTransformationGeometric Construction
In collections How to create a Tessellation (Rectangle)
This example demonstrates how to create a tessellation using GeoGebra. Key mathematical concepts include geometric transformations and vectors. Using commands such as Segment, OrthogonalLine, Point, Intersect, Vector, Translate, and Polygon, a beautiful tessellation can be constructed. Suitable for middle school and above students to learn geometric transformations and pattern design.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. OrthogonalLine(A, a) → b
  3. OrthogonalLine(B, a) → c
  4. Point(c) → D
  5. OrthogonalLine(D, b) → d
  6. Intersect(b, d) → F
  7. Segment(B, C) → e
  8. Segment(C, D) → f
  9. Vector(B, A) → u
  10. Translate(B, u) → B'
  11. Translate(C, u) → C'
  12. Segment(B', C') → e'
  13. Translate(C, u) → C'_1
  14. Translate(D, u) → D'
  15. Segment(C'_1, D') → f'
  16. Segment(F, E) → g
  17. Segment(E, D) → h
  18. Vector(F, A) → v
  19. Translate(F, v) → F'
  20. Translate(E, v) → E'
  21. Segment(F', E') → g'
  22. Translate(E, v) → E'_1
  23. Translate(D, v) → D'_1
  24. Segment(E'_1, D'_1) → h'
  25. Translate(D', v) → D''
  26. Polygon(A, E', B, C, D, E, F, C') → poly1, a_1, e'_1, b_1, c_1, d_1, e_1, f_1, c'
  27. Segment(I, J) → i
  28. Segment(J, K) → j
  29. Segment(K, L) → k
  30. Segment(L, M) → l
  31. Segment(M, N) → m
  32. Segment(N, O) → n
  33. Segment(I, P) → p
  34. Segment(P, Q) → q
  35. Segment(Q, R) → r
  36. Segment(R, S) → s
  37. Segment(S, O) → t
  38. Polygon(R, Q, S, P, I, J, K, L, M, N, O) → poly2, r_1, o, s_1, q_1, p_1, i_1, j_1, k_1, l_1, m_1, n_1
  39. Vector(A, D') → w
  40. Translate(A, w) → A'
  41. Translate(E', w) → E''
  42. Translate(B, w) → B'_1
  43. Translate(C, w) → C'_2
  44. Translate(D, w) → D'_2
  45. Translate(E, w) → E'_2
  46. Translate(F, w) → F'_1
  47. Translate(C', w) → C''
  48. Polygon(A', E'', B'_1, C'_2, D'_2, E'_2, F'_1, C'') → poly1', a', e'', b'_1, c'_2, d'_2, e'_2, f'_1, c''
  49. Translate(R, w) → R'
  50. Translate(Q, w) → Q'
  51. Translate(P, w) → P'
  52. Translate(I, w) → I'
  53. Translate(J, w) → J'
  54. Translate(K, w) → K'
  55. Translate(L, w) → L'
  56. Translate(M, w) → M'
  57. Translate(N, w) → N'
  58. Translate(O, w) → O'
  59. Translate(S, w) → S'
  60. Polygon(R', Q', S', P', I', J', K', L', M', N', O') → poly2', r', o', s', q', p', i', j', k', l', m', n'
  61. Translate(B, w) → B'_2
  62. Translate(C, w) → C'_3
  63. Segment(B'_2, C'_3) → e'_3
  64. Translate(C, w) → C'_4
  65. Translate(D, w) → D'_3
  66. Segment(C'_4, D'_3) → f'_2
  67. Translate(B', w) → B''
  68. Translate(C', w) → C''_1
  69. Segment(B'', C''_1) → e''_1
  70. Translate(C'_1, w) → T
  71. Translate(D', w) → D''_1
  72. Segment(T, D''_1) → f''
  73. Translate(F, w) → F'_2
  74. Translate(E, w) → E'_3
  75. Segment(F'_2, E'_3) → g'_1
  76. Translate(E, w) → E'_4
  77. Translate(D, w) → D'_4
  78. Segment(E'_4, D'_4) → h'_1
  79. Translate(F', w) → F''
  80. Translate(E', w) → E''_1
  81. Segment(F'', E''_1) → g''
  82. Translate(E'_1, w) → U
  83. Translate(D'_1, w) → V
  84. Segment(U, V) → h''
  85. Translate(G, w) → G'
  86. Translate(H, w) → H'
  87. Vector(A, D''_1) → u_1
  88. Translate(A, u_1) → A'_1
  89. Translate(E', u_1) → E''_2
  90. Translate(B, u_1) → B'_3
  91. Translate(C, u_1) → C'_5
  92. Translate(D, u_1) → D'_5
  93. Translate(E, u_1) → E'_5
  94. Translate(F, u_1) → F'_3
  95. Translate(C', u_1) → C''_2
  96. Polygon(A'_1, E''_2, B'_3, C'_5, D'_5, E'_5, F'_3, C''_2) → poly1'_1, a'_1, e''_2, b'_3, c'_5, d'_5, e'_5, f'_3, c''_2
  97. Translate(R, u_1) → R'_1
  98. Translate(Q, u_1) → Q'_1
  99. Translate(P, u_1) → P'_1
  100. Translate(I, u_1) → I'_1
  101. Translate(J, u_1) → J'_1
  102. Translate(K, u_1) → K'_1
  103. Translate(L, u_1) → L'_1
  104. Translate(M, u_1) → M'_1
  105. Translate(N, u_1) → N'_1
  106. Translate(O, u_1) → O'_1
  107. Translate(S, u_1) → S'_1
  108. Polygon(R'_1, Q'_1, S'_1, P'_1, I'_1, J'_1, K'_1, L'_1, M'_1, N'_1, O'_1) → poly2'_1, r'_1, o'_1, s'_1, q'_1, p'_1, i'_1, j'_1, k'_1, l'_1, m'_1, n'_1
  109. Translate(A', u_1) → A''
  110. Translate(E'', u_1) → E'''
  111. Translate(B'_1, u_1) → W
  112. Translate(C'_2, u_1) → Z
  113. Translate(D'_2, u_1) → A_1
  114. Translate(E'_2, u_1) → B_1
  115. Translate(F'_1, u_1) → C_1
  116. Translate(C'', u_1) → C'''
  117. Polygon(A'', E''', W, Z, A_1, B_1, C_1, C''') → poly1'', a'', e''', w_1, z, a_2, b_2, c_2, c'''
  118. Translate(R', u_1) → R''
  119. Translate(Q', u_1) → Q''
  120. Translate(P', u_1) → P''
  121. Translate(I', u_1) → I''
  122. Translate(J', u_1) → J''
  123. Translate(K', u_1) → K''
  124. Translate(L', u_1) → L''
  125. Translate(M', u_1) → M''
  126. Translate(N', u_1) → N''
  127. Translate(O', u_1) → O''
  128. Translate(S', u_1) → S''
  129. Polygon(R'', Q'', S'', P'', I'', J'', K'', L'', M'', N'', O'') → poly2'', r'', o'', s'', q'', p'', i'', j'', k'', l'', m'', n''
  130. Translate(B, u_1) → B'_4
  131. Translate(C, u_1) → C'_6
  132. Segment(B'_4, C'_6) → e'_4
  133. Translate(C, u_1) → C'_7
  134. Translate(D, u_1) → D'_6
  135. Segment(C'_7, D'_6) → f'_4
  136. Translate(B', u_1) → B''_1
  137. Translate(C', u_1) → C''_3
  138. Segment(B''_1, C''_3) → e''_3
  139. Translate(C'_1, u_1) → D_1
  140. Translate(D', u_1) → D''_2
  141. Segment(D_1, D''_2) → f''_1
  142. Translate(F, u_1) → F'_4
  143. Translate(E, u_1) → E'_6
  144. Segment(F'_4, E'_6) → g'_2
  145. Translate(E, u_1) → E'_7
  146. Translate(D, u_1) → D'_7
  147. Segment(E'_7, D'_7) → h'_2
  148. Translate(F', u_1) → F''_1
  149. Translate(E', u_1) → E''_3
  150. Segment(F''_1, E''_3) → g''_1
  151. Translate(E'_1, u_1) → E_1
  152. Translate(D'_1, u_1) → F_1
  153. Segment(E_1, F_1) → h''_1
  154. Translate(B'_2, u_1) → G_1
  155. Translate(C'_3, u_1) → H_1
  156. Segment(G_1, H_1) → g_1
  157. Translate(C'_4, u_1) → I_1
  158. Translate(D'_3, u_1) → J_1
  159. Segment(I_1, J_1) → h_1
  160. Translate(B'', u_1) → B'''
  161. Translate(C''_1, u_1) → K_1
  162. Segment(B''', K_1) → t_1
  163. Translate(T, u_1) → T'
  164. Translate(D''_1, u_1) → L_1
  165. Segment(T', L_1) → f'''
  166. Translate(F'_2, u_1) → M_1
  167. Translate(E'_3, u_1) → N_1
  168. Segment(M_1, N_1) → d_2
  169. Translate(E'_4, u_1) → O_1
  170. Translate(D'_4, u_1) → P_1
  171. Segment(O_1, P_1) → e_2
  172. Translate(F'', u_1) → F'''
  173. Translate(E''_1, u_1) → Q_1
  174. Segment(F''', Q_1) → g'''
  175. Translate(U, u_1) → U'
  176. Translate(V, u_1) → V'
  177. Segment(U', V') → h'''
  178. Translate(w, u_1) → w'
  179. Translate(G, u_1) → G'_1
  180. Translate(H, u_1) → H'_1
  181. Translate(G', u_1) → G''
  182. Translate(H', u_1) → H''
  183. Vector(A, B) → v_1
  184. Translate(A, v_1) → A'_2
  185. Translate(E', v_1) → E''_4
  186. Translate(B, v_1) → B'_5
  187. Translate(C, v_1) → C'_8
  188. Translate(D, v_1) → D'_8
  189. Translate(E, v_1) → E'_8
  190. Translate(F, v_1) → F'_5
  191. Translate(C', v_1) → C''_4
  192. Polygon(A'_2, E''_4, B'_5, C'_8, D'_8, E'_8, F'_5, C''_4) → poly1'_2, a'_2, e''_4, b'_5, c'_8, d'_8, e'_8, f'_5, c''_4
  193. Translate(R, v_1) → R'_2
  194. Translate(Q, v_1) → Q'_2
  195. Translate(P, v_1) → P'_2
  196. Translate(I, v_1) → I'_2
  197. Translate(J, v_1) → J'_2
  198. Translate(K, v_1) → K'_2
  199. Translate(L, v_1) → L'_2
  200. Translate(M, v_1) → M'_2
  201. Translate(N, v_1) → N'_2
  202. Translate(O, v_1) → O'_2
  203. Translate(S, v_1) → S'_2
  204. Polygon(R'_2, Q'_2, S'_2, P'_2, I'_2, J'_2, K'_2, L'_2, M'_2, N'_2, O'_2) → poly2'_2, r'_2, o'_2, s'_2, q'_2, p'_2, i'_2, j'_2, k'_2, l'_2, m'_2, n'_2
  205. Translate(A', v_1) → A''_1
  206. Translate(E'', v_1) → E'''_1
  207. Translate(B'_1, v_1) → R_1
  208. Translate(C'_2, v_1) → S_1
  209. Translate(D'_2, v_1) → T_1
  210. Translate(E'_2, v_1) → U_1
  211. Translate(F'_1, v_1) → V_1
  212. Translate(C'', v_1) → C'''_1
  213. Polygon(A''_1, E'''_1, R_1, S_1, T_1, U_1, V_1, C'''_1) → poly1''_1, a''_1, e'''_1, r_2, s_2, t_2, u_2, v_2, c'''_1
  214. Translate(R', v_1) → R''_1
  215. Translate(Q', v_1) → Q''_1
  216. Translate(P', v_1) → P''_1
  217. Translate(I', v_1) → I''_1
  218. Translate(J', v_1) → J''_1
  219. Translate(K', v_1) → K''_1
  220. Translate(L', v_1) → L''_1
  221. Translate(M', v_1) → M''_1
  222. Translate(N', v_1) → N''_1
  223. Translate(O', v_1) → O''_1
  224. Translate(S', v_1) → S''_1
  225. Polygon(R''_1, Q''_1, S''_1, P''_1, I''_1, J''_1, K''_1, L''_1, M''_1, N''_1, O''_1) → poly2''_1, r''_1, o''_1, s''_1, q''_1, p''_1, i''_1, j''_1, k''_1, l''_1, m''_1, n''_1
  226. Translate(A'_1, v_1) → W_1
  227. Translate(E''_2, v_1) → Z_1
  228. Translate(B'_3, v_1) → A_2
  229. Translate(C'_5, v_1) → B_2
  230. Translate(D'_5, v_1) → C_2
  231. Translate(E'_5, v_1) → D_2
  232. Translate(F'_3, v_1) → E_2
  233. Translate(C''_2, v_1) → F_2
  234. Polygon(W_1, Z_1, A_2, B_2, C_2, D_2, E_2, F_2) → poly3, w_2, z_1, a_3, b_3, c_3, d_3, e_3, f_2
  235. Translate(R'_1, v_1) → G_2
  236. Translate(Q'_1, v_1) → H_2
  237. Translate(P'_1, v_1) → I_2
  238. Translate(I'_1, v_1) → J_2
  239. Translate(J'_1, v_1) → K_2
  240. Translate(K'_1, v_1) → L_2
  241. Translate(L'_1, v_1) → M_2
  242. Translate(M'_1, v_1) → N_2
  243. Translate(N'_1, v_1) → O_2
  244. Translate(O'_1, v_1) → P_2
  245. Translate(S'_1, v_1) → Q_2
  246. Polygon(G_2, H_2, Q_2, I_2, J_2, K_2, L_2, M_2, N_2, O_2, P_2) → poly4, g_2, p_2, q_2, h_2, i_2, j_2, k_2, l_2, m_2, n_2, o_2
  247. Translate(A'', v_1) → A'''
  248. Translate(E''', v_1) → R_2
  249. Translate(W, v_1) → W'
  250. Translate(Z, v_1) → Z'
  251. Translate(A_1, v_1) → S_2
  252. Translate(B_1, v_1) → T_2
  253. Translate(C_1, v_1) → U_2
  254. Translate(C''', v_1) → V_2
  255. Polygon(A''', R_2, W', Z', S_2, T_2, U_2, V_2) → poly1''', a''', r_3, w'_1, z', s_3, t_3, u_3, v_3
  256. Translate(R'', v_1) → R'''
  257. Translate(Q'', v_1) → Q'''
  258. Translate(P'', v_1) → P'''
  259. Translate(I'', v_1) → I'''
  260. Translate(J'', v_1) → J'''
  261. Translate(K'', v_1) → K'''
  262. Translate(L'', v_1) → L'''
  263. Translate(M'', v_1) → M'''
  264. Translate(N'', v_1) → N'''
  265. Translate(O'', v_1) → O'''
  266. Translate(S'', v_1) → S'''
  267. Polygon(R''', Q''', S''', P''', I''', J''', K''', L''', M''', N''', O''') → poly2''', r''', o''', s''', q''', p''', i''', j''', k''', l''', m''', n'''
  268. Translate(B, v_1) → B'_6
  269. Translate(C, v_1) → C'_9
  270. Segment(B'_6, C'_9) → e'_6
  271. Translate(C, v_1) → C'_{10}
  272. Translate(D, v_1) → D'_9
  273. Segment(C'_{10}, D'_9) → f'_6
  274. Translate(B', v_1) → B''_2
  275. Translate(C', v_1) → C''_5
  276. Segment(B''_2, C''_5) → e''_5
  277. Translate(C'_1, v_1) → W_2
  278. Translate(D', v_1) → D''_3
  279. Segment(W_2, D''_3) → f''_2
  280. Translate(F, v_1) → F'_6
  281. Translate(E, v_1) → E'_9
  282. Segment(F'_6, E'_9) → g'_3
  283. Translate(E, v_1) → E'_{10}
  284. Translate(D, v_1) → D'_{10}
  285. Segment(E'_{10}, D'_{10}) → h'_3
  286. Translate(F', v_1) → F''_2
  287. Translate(E', v_1) → E''_5
  288. Segment(F''_2, E''_5) → g''_2
  289. Translate(E'_1, v_1) → Z_2
  290. Translate(D'_1, v_1) → A_3
  291. Segment(Z_2, A_3) → h''_2
  292. Translate(B'_2, v_1) → B_3
  293. Translate(C'_3, v_1) → C_3
  294. Segment(B_3, C_3) → f_3
  295. Translate(C'_4, v_1) → D_3
  296. Translate(D'_3, v_1) → E_3
  297. Segment(D_3, E_3) → g_3
  298. Translate(B'', v_1) → B'''_1
  299. Translate(C''_1, v_1) → F_3
  300. Segment(B'''_1, F_3) → h_3
  301. Translate(T, v_1) → T'_1
  302. Translate(D''_1, v_1) → G_3
  303. Segment(T'_1, G_3) → f'''_1
  304. Translate(F'_2, v_1) → H_3
  305. Translate(E'_3, v_1) → I_3
  306. Segment(H_3, I_3) → i_3
  307. Translate(E'_4, v_1) → J_3
  308. Translate(D'_4, v_1) → K_3
  309. Segment(J_3, K_3) → j_3
  310. Translate(F'', v_1) → F'''_1
  311. Translate(E''_1, v_1) → L_3
  312. Segment(F'''_1, L_3) → g'''_1
  313. Translate(U, v_1) → U'_1
  314. Translate(V, v_1) → V'_1
  315. Segment(U'_1, V'_1) → h'''_1
  316. Translate(B'_4, v_1) → M_3
  317. Translate(C'_6, v_1) → N_3
  318. Segment(M_3, N_3) → k_3
  319. Translate(C'_7, v_1) → O_3
  320. Translate(D'_6, v_1) → P_3
  321. Segment(O_3, P_3) → l_3
  322. Translate(B''_1, v_1) → Q_3
  323. Translate(C''_3, v_1) → R_3
  324. Segment(Q_3, R_3) → m_3
  325. Translate(D_1, v_1) → S_3
  326. Translate(D''_2, v_1) → T_3
  327. Segment(S_3, T_3) → n_3
  328. Translate(F'_4, v_1) → U_3
  329. Translate(E'_6, v_1) → V_3
  330. Segment(U_3, V_3) → p_3
  331. Translate(E'_7, v_1) → W_3
  332. Translate(D'_7, v_1) → Z_3
  333. Segment(W_3, Z_3) → q_3
  334. Translate(F''_1, v_1) → A_4
  335. Translate(E''_3, v_1) → B_4
  336. Segment(A_4, B_4) → a_4
  337. Translate(E_1, v_1) → C_4
  338. Translate(F_1, v_1) → D_4
  339. Segment(C_4, D_4) → b_4
  340. Translate(G_1, v_1) → E_4
  341. Translate(H_1, v_1) → F_4
  342. Segment(E_4, F_4) → c_4
  343. Translate(I_1, v_1) → G_4
  344. Translate(J_1, v_1) → H_4
  345. Segment(G_4, H_4) → d_4
  346. Translate(B''', v_1) → I_4
  347. Translate(K_1, v_1) → J_4
  348. Segment(I_4, J_4) → e_4
  349. Translate(T', v_1) → T''
  350. Translate(L_1, v_1) → K_4
  351. Segment(T'', K_4) → f_4
  352. Translate(M_1, v_1) → L_4
  353. Translate(N_1, v_1) → M_4
  354. Segment(L_4, M_4) → g_4
  355. Translate(O_1, v_1) → N_4
  356. Translate(P_1, v_1) → O_4
  357. Segment(N_4, O_4) → h_4
  358. Translate(F''', v_1) → P_4
  359. Translate(Q_1, v_1) → Q_4
  360. Segment(P_4, Q_4) → i_4
  361. Translate(U', v_1) → U''
  362. Translate(V', v_1) → V''
  363. Segment(U'', V'') → j_4
  364. Translate(w, v_1) → w'_2
  365. Translate(u_1, v_1) → w_3
  366. Translate(w', v_1) → w''
  367. Translate(G, v_1) → G'_2
  368. Translate(H, v_1) → H'_2
  369. Translate(G', v_1) → G''_1
  370. Translate(H', v_1) → H''_1
  371. Translate(G'_1, v_1) → R_4
  372. Translate(H'_1, v_1) → S_4
  373. Translate(G'', v_1) → G'''
  374. Translate(H'', v_1) → H'''
  375. Vector(A, B'_5) → u_4
  376. Translate(A, u_4) → A'_3
  377. Translate(E', u_4) → E''_6
  378. Translate(B, u_4) → B'_7
  379. Translate(C, u_4) → C'_{11}
  380. Translate(D, u_4) → D'_{11}
  381. Translate(E, u_4) → E'_{11}
  382. Translate(F, u_4) → F'_7
  383. Translate(C', u_4) → C''_6
  384. Polygon(A'_3, E''_6, B'_7, C'_{11}, D'_{11}, E'_{11}, F'_7, C''_6) → poly1'_3, a'_3, e''_6, b'_7, c'_{11}, d'_{11}, e'_{11}, f'_7, c''_6
  385. Translate(R, u_4) → R'_3
  386. Translate(Q, u_4) → Q'_3
  387. Translate(P, u_4) → P'_3
  388. Translate(I, u_4) → I'_3
  389. Translate(J, u_4) → J'_3
  390. Translate(K, u_4) → K'_3
  391. Translate(L, u_4) → L'_3
  392. Translate(M, u_4) → M'_3
  393. Translate(N, u_4) → N'_3
  394. Translate(O, u_4) → O'_3
  395. Translate(S, u_4) → S'_3
  396. Polygon(R'_3, Q'_3, S'_3, P'_3, I'_3, J'_3, K'_3, L'_3, M'_3, N'_3, O'_3) → poly2'_3, r'_3, o'_3, s'_3, q'_3, p'_3, i'_3, j'_3, k'_3, l'_3, m'_3, n'_3
  397. Translate(A', u_4) → A''_2
  398. Translate(E'', u_4) → E'''_2
  399. Translate(B'_1, u_4) → T_4
  400. Translate(C'_2, u_4) → U_4
  401. Translate(D'_2, u_4) → V_4
  402. Translate(E'_2, u_4) → W_4
  403. Translate(F'_1, u_4) → Z_4
  404. Translate(C'', u_4) → C'''_2
  405. Polygon(A''_2, E'''_2, T_4, U_4, V_4, W_4, Z_4, C'''_2) → poly1''_2, a''_2, e'''_2, t_4, u_5, v_4, w_4, z_4, c'''_2
  406. Translate(R', u_4) → R''_2
  407. Translate(Q', u_4) → Q''_2
  408. Translate(P', u_4) → P''_2
  409. Translate(I', u_4) → I''_2
  410. Translate(J', u_4) → J''_2
  411. Translate(K', u_4) → K''_2
  412. Translate(L', u_4) → L''_2
  413. Translate(M', u_4) → M''_2
  414. Translate(N', u_4) → N''_2
  415. Translate(O', u_4) → O''_2
  416. Translate(S', u_4) → S''_2
  417. Polygon(R''_2, Q''_2, S''_2, P''_2, I''_2, J''_2, K''_2, L''_2, M''_2, N''_2, O''_2) → poly2''_2, r''_2, o''_2, s''_2, q''_2, p''_2, i''_2, j''_2, k''_2, l''_2, m''_2, n''_2
  418. Translate(A'_1, u_4) → A_5
  419. Translate(E''_2, u_4) → B_5
  420. Translate(B'_3, u_4) → C_5
  421. Translate(C'_5, u_4) → D_5
  422. Translate(D'_5, u_4) → E_5
  423. Translate(E'_5, u_4) → F_5
  424. Translate(F'_3, u_4) → G_5
  425. Translate(C''_2, u_4) → H_5
  426. Polygon(A_5, B_5, C_5, D_5, E_5, F_5, G_5, H_5) → poly5, a_5, b_5, c_5, d_5, e_5, f_5, g_5, h_5
  427. Translate(R'_1, u_4) → I_5
  428. Translate(Q'_1, u_4) → J_5
  429. Translate(P'_1, u_4) → K_5
  430. Translate(I'_1, u_4) → L_5
  431. Translate(J'_1, u_4) → M_5
  432. Translate(K'_1, u_4) → N_5
  433. Translate(L'_1, u_4) → O_5
  434. Translate(M'_1, u_4) → P_5
  435. Translate(N'_1, u_4) → Q_5
  436. Translate(O'_1, u_4) → R_5
  437. Translate(S'_1, u_4) → S_5
  438. Polygon(I_5, J_5, S_5, K_5, L_5, M_5, N_5, O_5, P_5, Q_5, R_5) → poly6, i_5, r_5, s_5, j_5, k_5, l_5, m_5, n_5, o_5, p_5, q_5
  439. Translate(A'', u_4) → A'''_1
  440. Translate(E''', u_4) → T_5
  441. Translate(W, u_4) → W'_1
  442. Translate(Z, u_4) → Z'_1
  443. Translate(A_1, u_4) → U_5
  444. Translate(B_1, u_4) → V_5
  445. Translate(C_1, u_4) → W_5
  446. Translate(C''', u_4) → Z_5
  447. Polygon(A'''_1, T_5, W'_1, Z'_1, U_5, V_5, W_5, Z_5) → poly1'''_1, a'''_1, t_5, w'_3, z'_1, u_6, v_5, w_5, z_5
  448. Translate(R'', u_4) → R'''_1
  449. Translate(Q'', u_4) → Q'''_1
  450. Translate(P'', u_4) → P'''_1
  451. Translate(I'', u_4) → I'''_1
  452. Translate(J'', u_4) → J'''_1
  453. Translate(K'', u_4) → K'''_1
  454. Translate(L'', u_4) → L'''_1
  455. Translate(M'', u_4) → M'''_1
  456. Translate(N'', u_4) → N'''_1
  457. Translate(O'', u_4) → O'''_1
  458. Translate(S'', u_4) → S'''_1
  459. Polygon(R'''_1, Q'''_1, S'''_1, P'''_1, I'''_1, J'''_1, K'''_1, L'''_1, M'''_1, N'''_1, O'''_1) → poly2'''_1, r'''_1, o'''_1, s'''_1, q'''_1, p'''_1, i'''_1, j'''_1, k'''_1, l'''_1, m'''_1, n'''_1
  460. Translate(A'_2, u_4) → A_6
  461. Translate(E''_4, u_4) → B_6
  462. Translate(B'_5, u_4) → C_6
  463. Translate(C'_8, u_4) → D_6
  464. Translate(D'_8, u_4) → E_6
  465. Translate(E'_8, u_4) → F_6
  466. Translate(F'_5, u_4) → G_6
  467. Translate(C''_4, u_4) → H_6
  468. Polygon(A_6, B_6, C_6, D_6, E_6, F_6, G_6, H_6) → poly7, a_6, b_6, c_6, d_6, e_6, f_6, g_6, h_6
  469. Translate(R'_2, u_4) → I_6
  470. Translate(Q'_2, u_4) → J_6
  471. Translate(P'_2, u_4) → K_6
  472. Translate(I'_2, u_4) → L_6
  473. Translate(J'_2, u_4) → M_6
  474. Translate(K'_2, u_4) → N_6
  475. Translate(L'_2, u_4) → O_6
  476. Translate(M'_2, u_4) → P_6
  477. Translate(N'_2, u_4) → Q_6
  478. Translate(O'_2, u_4) → R_6
  479. Translate(S'_2, u_4) → S_6
  480. Polygon(I_6, J_6, S_6, K_6, L_6, M_6, N_6, O_6, P_6, Q_6, R_6) → poly8, i_6, r_6, s_6, j_6, k_6, l_6, m_6, n_6, o_6, p_6, q_6
  481. Translate(A''_1, u_4) → T_6
  482. Translate(E'''_1, u_4) → U_6
  483. Translate(R_1, u_4) → V_6
  484. Translate(S_1, u_4) → W_6
  485. Translate(T_1, u_4) → Z_6
  486. Translate(U_1, u_4) → A_7
  487. Translate(V_1, u_4) → B_7
  488. Translate(C'''_1, u_4) → C_7
  489. Polygon(T_6, U_6, V_6, W_6, Z_6, A_7, B_7, C_7) → poly9, t_6, u_7, v_6, w_6, z_6, a_7, b_7, c_7
  490. Translate(R''_1, u_4) → D_7
  491. Translate(Q''_1, u_4) → E_7
  492. Translate(P''_1, u_4) → F_7
  493. Translate(I''_1, u_4) → G_7
  494. Translate(J''_1, u_4) → H_7
  495. Translate(K''_1, u_4) → I_7
  496. Translate(L''_1, u_4) → J_7
  497. Translate(M''_1, u_4) → K_7
  498. Translate(N''_1, u_4) → L_7
  499. Translate(O''_1, u_4) → M_7
  500. Translate(S''_1, u_4) → N_7
  501. Polygon(D_7, E_7, N_7, F_7, G_7, H_7, I_7, J_7, K_7, L_7, M_7) → poly10, d_7, m_7, n_7, e_7, f_7, g_7, h_7, i_7, j_7, k_7, l_7
  502. Translate(W_1, u_4) → O_7
  503. Translate(Z_1, u_4) → P_7
  504. Translate(A_2, u_4) → Q_7
  505. Translate(B_2, u_4) → R_7
  506. Translate(C_2, u_4) → S_7
  507. Translate(D_2, u_4) → T_7
  508. Translate(E_2, u_4) → U_7
  509. Translate(F_2, u_4) → V_7
  510. Polygon(O_7, P_7, Q_7, R_7, S_7, T_7, U_7, V_7) → poly3', o_7, p_7, q_7, r_7, s_7, t_7, u_8, v_7
  511. Translate(G_2, u_4) → W_7
  512. Translate(H_2, u_4) → Z_7
  513. Translate(I_2, u_4) → A_8
  514. Translate(J_2, u_4) → B_8
  515. Translate(K_2, u_4) → C_8
  516. Translate(L_2, u_4) → D_8
  517. Translate(M_2, u_4) → E_8
  518. Translate(N_2, u_4) → F_8
  519. Translate(O_2, u_4) → G_8
  520. Translate(P_2, u_4) → H_8
  521. Translate(Q_2, u_4) → I_8
  522. Polygon(W_7, Z_7, I_8, A_8, B_8, C_8, D_8, E_8, F_8, G_8, H_8) → poly4', w_7, h_8, i_8, z_7, a_8, b_8, c_8, d_8, e_8, f_8, g_8
  523. Translate(A''', u_4) → J_8
  524. Translate(R_2, u_4) → K_8
  525. Translate(W', u_4) → W''
  526. Translate(Z', u_4) → Z''
  527. Translate(S_2, u_4) → L_8
  528. Translate(T_2, u_4) → M_8
  529. Translate(U_2, u_4) → N_8
  530. Translate(V_2, u_4) → O_8
  531. Polygon(J_8, K_8, W'', Z'', L_8, M_8, N_8, O_8) → poly11, j_8, k_8, w''_1, z'', l_8, m_8, n_8, o_8
  532. Translate(R''', u_4) → P_8
  533. Translate(Q''', u_4) → Q_8
  534. Translate(P''', u_4) → R_8
  535. Translate(I''', u_4) → S_8
  536. Translate(J''', u_4) → T_8
  537. Translate(K''', u_4) → U_8
  538. Translate(L''', u_4) → V_8
  539. Translate(M''', u_4) → W_8
  540. Translate(N''', u_4) → Z_8
  541. Translate(O''', u_4) → A_9
  542. Translate(S''', u_4) → B_9
  543. Polygon(P_8, Q_8, B_9, R_8, S_8, T_8, U_8, V_8, W_8, Z_8, A_9) → poly12, p_8, a_9, b_9, q_8, r_8, s_8, t_8, u_9, v_8, w_8, z_8
  544. Translate(B, u_4) → B'_8
  545. Translate(C, u_4) → C'_{12}
  546. Segment(B'_8, C'_{12}) → e'_7
  547. Translate(C, u_4) → C'_{13}
  548. Translate(D, u_4) → D'_{12}
  549. Segment(C'_{13}, D'_{12}) → f'_8
  550. Translate(B', u_4) → B''_3
  551. Translate(C', u_4) → C''_7
  552. Segment(B''_3, C''_7) → e''_7
  553. Translate(C'_1, u_4) → C_9
  554. Translate(D', u_4) → D''_4
  555. Segment(C_9, D''_4) → f''_3
  556. Translate(F, u_4) → F'_8
  557. Translate(E, u_4) → E'_{12}
  558. Segment(F'_8, E'_{12}) → g'_4
  559. Translate(E, u_4) → E'_{13}
  560. Translate(D, u_4) → D'_{13}
  561. Segment(E'_{13}, D'_{13}) → h'_4
  562. Translate(F', u_4) → F''_3
  563. Translate(E', u_4) → E''_7
  564. Segment(F''_3, E''_7) → g''_3
  565. Translate(E'_1, u_4) → D_9
  566. Translate(D'_1, u_4) → E_9
  567. Segment(D_9, E_9) → h''_3
  568. Translate(B'_2, u_4) → F_9
  569. Translate(C'_3, u_4) → G_9
  570. Segment(F_9, G_9) → k_4
  571. Translate(D'_3, u_4) → I_9
  572. Translate(B'', u_4) → B'''_2
  573. Translate(C''_1, u_4) → J_9
  574. Segment(B'''_2, J_9) → m_4
  575. Translate(T, u_4) → T'_2
  576. Translate(D''_1, u_4) → K_9
  577. Segment(T'_2, K_9) → f'''_2
  578. Translate(F'_2, u_4) → L_9
  579. Translate(E'_3, u_4) → M_9
  580. Segment(L_9, M_9) → n_4
  581. Translate(E'_4, u_4) → N_9
  582. Translate(D'_4, u_4) → O_9
  583. Segment(N_9, O_9) → p_4
  584. Translate(F'', u_4) → F'''_2
  585. Translate(E''_1, u_4) → P_9
  586. Segment(F'''_2, P_9) → g'''_2
  587. Translate(U, u_4) → U'_2
  588. Translate(V, u_4) → V'_2
  589. Segment(U'_2, V'_2) → h'''_2
  590. Translate(B'_4, u_4) → Q_9
  591. Translate(C'_6, u_4) → R_9
  592. Segment(Q_9, R_9) → q_4
  593. Translate(C'_7, u_4) → S_9
  594. Translate(D'_6, u_4) → T_9
  595. Segment(S_9, T_9) → r_4
  596. Translate(B''_1, u_4) → U_9
  597. Translate(C''_3, u_4) → V_9
  598. Segment(U_9, V_9) → s_4
  599. Translate(D_1, u_4) → W_9
  600. Translate(D''_2, u_4) → Z_9
  601. Segment(W_9, Z_9) → c_9
  602. Translate(F'_4, u_4) → A_{10}
  603. Translate(E'_6, u_4) → B_{10}
  604. Segment(A_{10}, B_{10}) → d_9
  605. Translate(E'_7, u_4) → C_{10}
  606. Translate(D'_7, u_4) → D_{10}
  607. Segment(C_{10}, D_{10}) → e_9
  608. Translate(F''_1, u_4) → E_{10}
  609. Translate(E''_3, u_4) → F_{10}
  610. Segment(E_{10}, F_{10}) → f_9
  611. Translate(E_1, u_4) → G_{10}
  612. Translate(F_1, u_4) → H_{10}
  613. Segment(G_{10}, H_{10}) → g_9
  614. Translate(G_1, u_4) → I_{10}
  615. Translate(H_1, u_4) → J_{10}
  616. Segment(I_{10}, J_{10}) → h_9
  617. Translate(I_1, u_4) → K_{10}
  618. Translate(J_1, u_4) → L_{10}
  619. Segment(K_{10}, L_{10}) → i_9
  620. Translate(B''', u_4) → M_{10}
  621. Translate(K_1, u_4) → N_{10}
  622. Segment(M_{10}, N_{10}) → j_9
  623. Translate(T', u_4) → T''_1
  624. Translate(L_1, u_4) → O_{10}
  625. Segment(T''_1, O_{10}) → k_9
  626. Translate(M_1, u_4) → P_{10}
  627. Translate(N_1, u_4) → Q_{10}
  628. Segment(P_{10}, Q_{10}) → l_9
  629. Translate(O_1, u_4) → R_{10}
  630. Translate(P_1, u_4) → S_{10}
  631. Segment(R_{10}, S_{10}) → m_9
  632. Translate(F''', u_4) → T_{10}
  633. Translate(Q_1, u_4) → U_{10}
  634. Segment(T_{10}, U_{10}) → n_9
  635. Translate(U', u_4) → U''_1
  636. Translate(V', u_4) → V''_1
  637. Segment(U''_1, V''_1) → p_9
  638. Translate(B'_6, u_4) → V_{10}
  639. Translate(C'_9, u_4) → W_{10}
  640. Segment(V_{10}, W_{10}) → q_9
  641. Translate(C'_{10}, u_4) → Z_{10}
  642. Translate(D'_9, u_4) → A_{11}
  643. Segment(Z_{10}, A_{11}) → r_9
  644. Translate(B''_2, u_4) → B_{11}
  645. Translate(C''_5, u_4) → C_{11}
  646. Segment(B_{11}, C_{11}) → s_9
  647. Translate(W_2, u_4) → D_{11}
  648. Translate(D''_3, u_4) → E_{11}
  649. Segment(D_{11}, E_{11}) → t_9
  650. Translate(F'_6, u_4) → F_{11}
  651. Translate(E'_9, u_4) → G_{11}
  652. Segment(F_{11}, G_{11}) → a_{10}
  653. Translate(D'_{10}, u_4) → I_{11}
  654. Translate(F''_2, u_4) → J_{11}
  655. Translate(E''_5, u_4) → K_{11}
  656. Segment(J_{11}, K_{11}) → c_{10}
  657. Translate(Z_2, u_4) → L_{11}
  658. Translate(A_3, u_4) → M_{11}
  659. Segment(L_{11}, M_{11}) → d_{10}
  660. Translate(B_3, u_4) → N_{11}
  661. Translate(C_3, u_4) → O_{11}
  662. Segment(N_{11}, O_{11}) → e_{10}
  663. Translate(D_3, u_4) → P_{11}
  664. Translate(E_3, u_4) → Q_{11}
  665. Segment(P_{11}, Q_{11}) → f_{10}
  666. Translate(B'''_1, u_4) → R_{11}
  667. Translate(F_3, u_4) → S_{11}
  668. Segment(R_{11}, S_{11}) → g_{10}
  669. Translate(T'_1, u_4) → T_{11}
  670. Translate(G_3, u_4) → U_{11}
  671. Segment(T_{11}, U_{11}) → h_{10}
  672. Translate(H_3, u_4) → V_{11}
  673. Translate(I_3, u_4) → W_{11}
  674. Segment(V_{11}, W_{11}) → i_{10}
  675. Translate(J_3, u_4) → Z_{11}
  676. Translate(K_3, u_4) → A_{12}
  677. Segment(Z_{11}, A_{12}) → j_{10}
  678. Translate(F'''_1, u_4) → B_{12}
  679. Translate(L_3, u_4) → C_{12}
  680. Segment(B_{12}, C_{12}) → k_{10}
  681. Translate(U'_1, u_4) → D_{12}
  682. Translate(V'_1, u_4) → E_{12}
  683. Segment(D_{12}, E_{12}) → l_{10}
  684. Translate(M_3, u_4) → F_{12}
  685. Translate(N_3, u_4) → G_{12}
  686. Segment(F_{12}, G_{12}) → m_{10}
  687. Translate(O_3, u_4) → H_{12}
  688. Translate(P_3, u_4) → I_{12}
  689. Segment(H_{12}, I_{12}) → n_{10}
  690. Translate(Q_3, u_4) → J_{12}
  691. Translate(S_3, u_4) → L_{12}
  692. Translate(T_3, u_4) → M_{12}
  693. Segment(L_{12}, M_{12}) → q_{10}
  694. Translate(U_3, u_4) → N_{12}
  695. Translate(V_3, u_4) → O_{12}
  696. Segment(N_{12}, O_{12}) → r_{10}
  697. Translate(W_3, u_4) → P_{12}
  698. Translate(Z_3, u_4) → Q_{12}
  699. Segment(P_{12}, Q_{12}) → s_{10}
  700. Translate(A_4, u_4) → R_{12}
  701. Translate(B_4, u_4) → S_{12}
  702. Segment(R_{12}, S_{12}) → t_{10}
  703. Translate(C_4, u_4) → T_{12}
  704. Translate(D_4, u_4) → U_{12}
  705. Segment(T_{12}, U_{12}) → a_{11}
  706. Translate(E_4, u_4) → V_{12}
  707. Translate(F_4, u_4) → W_{12}
  708. Segment(V_{12}, W_{12}) → b_{11}
  709. Translate(G_4, u_4) → Z_{12}
  710. Translate(H_4, u_4) → A_{13}
  711. Segment(Z_{12}, A_{13}) → c_{11}
  712. Translate(I_4, u_4) → B_{13}
  713. Translate(J_4, u_4) → C_{13}
  714. Segment(B_{13}, C_{13}) → d_{11}
  715. Translate(T'', u_4) → T'''
  716. Translate(K_4, u_4) → D_{13}
  717. Segment(T''', D_{13}) → e_{11}
  718. Translate(L_4, u_4) → E_{13}
  719. Translate(M_4, u_4) → F_{13}
  720. Segment(E_{13}, F_{13}) → f_{11}
  721. Translate(N_4, u_4) → G_{13}
  722. Translate(O_4, u_4) → H_{13}
  723. Segment(G_{13}, H_{13}) → g_{11}
  724. Translate(P_4, u_4) → I_{13}
  725. Translate(U'', u_4) → U'''
  726. Translate(V'', u_4) → V'''
  727. Segment(U''', V''') → i_{11}
  728. Translate(w, u_4) → w'_4
  729. Translate(u_1, u_4) → v_9
  730. Translate(w', u_4) → w''_2
  731. Translate(v_1, u_4) → w_9
  732. Translate(w'_2, u_4) → u_{10}
  733. Translate(w_3, u_4) → v_{10}
  734. Translate(w'', u_4) → w'''
  735. Translate(G, u_4) → G'_3
  736. Translate(H, u_4) → H'_3
  737. Translate(G', u_4) → G''_2
  738. Translate(H', u_4) → H''_2
  739. Translate(G'_1, u_4) → K_{13}
  740. Translate(H'_1, u_4) → L_{13}
  741. Translate(G'', u_4) → G'''_1
  742. Translate(H'', u_4) → H'''_1
  743. Translate(G'_2, u_4) → M_{13}
  744. Translate(H'_2, u_4) → N_{13}
  745. Translate(G''_1, u_4) → O_{13}
  746. Translate(H''_1, u_4) → P_{13}
  747. Translate(R_4, u_4) → Q_{13}
  748. Translate(S_4, u_4) → R_{13}
  749. Translate(G''', u_4) → S_{13}
  750. Translate(H''', u_4) → T_{13}

AI Drawing Prompt Reference

Create a hexagonal tessellation. Start by drawing points A and B, then draw the perpendicular bisector b of AB and c through D on c. Draw the perpendicular bisector d of BD and find the intersection F of b and d. Draw line segments BC and CD, then translate B and C along vector BA to get B' and C'. Draw the line segment B'C'. Continue by translating C and D to get C'1 and D', and draw the line segment C'1D'. Draw the perpendicular bisector v of FA and translate F along v to get F'. Draw the line segment E'F'. Translate E and D to get E'1 and D'1, and draw the line segment E'1D'1. Finally, draw the polygon with points A, E', B, C, D, E, F, and C', and the polygon with points R, Q, S, P, I, J, K, L, M, N, and O, then translate A, E', B'1, C'2, D'2, E'2, F'1, and C'' to form the final tessellation.
The prompt above was compiled from the original drawing commands and is for reference only.