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Escher-like polygon tiling via rotation and translation

Escher-like polygon tiling via rotation and translation
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2023-03-20 23:29
PolygonAngleVectorTransformationGeometric Construction
In collections geometriadinamica.es
This example demonstrates how to build an Escher-like tiling by repeatedly applying geometric transformations to a base polygon unit. The key ideas are polygon vertex construction, vector-based translation (using vectors to encode direction and magnitude), and rotation as a rigid transformation around a chosen center. By chaining these operations with suitable parameters, the diagram generates a coherent pattern of repeated structure. Construction follows the provided GeoGebra commands and objects: Polygon creates the initial polygon; Vector defines translation directions; Rotate performs rotational copies of the polygon around a specified point/center; Translate moves copies according to the defined vectors, producing a nested, continuous layout. The workspace also includes multiple labeled points (e.g., A–Z and indexed variants) and auxiliary elements used as inputs to the transformations. Suitable for advanced middle school through introductory university geometry, especially for teaching transformation geometry, geometric construction, and interactive visual reasoning.

GeoGebra Commands & Parameters

  1. Polygon(A, B, K, L, M, N, O, P, Q, R, S, T, C, U, V, W, Y, Z, A_1, B_1, C_1, D_1, E_1, D, F_1, G_1, H_1, I_1, J_1, K_1, L_1, M_1, N_1, O_1, E, P_4, Q_1, R_1, S_1, T_1, U_1, V_1, W_1, Y_1, Z_1, F, A_2, B_2, C_2, D_2, E_2, G, H, I, J) → P_1, a, j, k, l, m, n, p, q, r, s, t, b, a_1, b_1, c_1, d_1, e_1, f_1, g_1, h_1, i_1, j_1, c, k_1, l_1, m_1, n_1, p_1, q_1, r_1, s_1, t_1, b_2, d, c_2, d_2, e_2, f_2, g_2, h_2, i_2, j_2, k_2, l_2, e, m_2, n_2, p_2, q_2, r_2, s_2, f, g, h, i
  2. Rotate(A, α, A) → A'
  3. Rotate(B, α, A) → B'
  4. Rotate(C, α, A) → C'
  5. Rotate(D, α, A) → D'
  6. Rotate(E, α, A) → E'
  7. Rotate(F, α, A) → F'
  8. Rotate(G, α, A) → G'
  9. Rotate(H, α, A) → H'
  10. Rotate(I, α, A) → I'
  11. Rotate(J, α, A) → J'
  12. Rotate(K, α, A) → K'
  13. Rotate(L, α, A) → L'
  14. Rotate(M, α, A) → M'
  15. Rotate(N, α, A) → N'
  16. Rotate(O, α, A) → O'
  17. Rotate(P, α, A) → P'
  18. Rotate(Q, α, A) → Q'
  19. Rotate(R, α, A) → R'
  20. Rotate(S, α, A) → S'
  21. Rotate(T, α, A) → T'
  22. Rotate(U, α, A) → U'
  23. Rotate(V, α, A) → V'
  24. Rotate(W, α, A) → W'
  25. Rotate(Y, α, A) → Y'
  26. Rotate(Z, α, A) → Z'
  27. Rotate(A_1, α, A) → A_1'
  28. Rotate(B_1, α, A) → B_1'
  29. Rotate(C_1, α, A) → C_1'
  30. Rotate(D_1, α, A) → D_1'
  31. Rotate(E_1, α, A) → E_1'
  32. Rotate(F_1, α, A) → F_1'
  33. Rotate(G_1, α, A) → G_1'
  34. Rotate(H_1, α, A) → H_1'
  35. Rotate(I_1, α, A) → I_1'
  36. Rotate(J_1, α, A) → J_1'
  37. Rotate(K_1, α, A) → K_1'
  38. Rotate(L_1, α, A) → L_1'
  39. Rotate(M_1, α, A) → M_1'
  40. Rotate(N_1, α, A) → N_1'
  41. Rotate(O_1, α, A) → O_1'
  42. Rotate(P_4, α, A) → P_1'
  43. Rotate(Q_1, α, A) → Q_1'
  44. Rotate(R_1, α, A) → R_1'
  45. Rotate(S_1, α, A) → S_1'
  46. Rotate(T_1, α, A) → T_1'
  47. Rotate(U_1, α, A) → U_1'
  48. Rotate(V_1, α, A) → V_1'
  49. Rotate(W_1, α, A) → W_1'
  50. Rotate(Y_1, α, A) → Y_1'
  51. Rotate(Z_1, α, A) → Z_1'
  52. Rotate(A_2, α, A) → A_2'
  53. Rotate(B_2, α, A) → B_2'
  54. Rotate(C_2, α, A) → C_2'
  55. Rotate(D_2, α, A) → D_2'
  56. Rotate(E_2, α, A) → E_2'
  57. Polygon(A', B', K', L', M', N', O', P', Q', R', S', T', C', U', V', W', Y', Z', A_1', B_1', C_1', D_1', E_1', D', F_1', G_1', H_1', I_1', J_1', K_1', L_1', M_1', N_1', O_1', E', P_1', Q_1', R_1', S_1', T_1', U_1', V_1', W_1', Y_1', Z_1', F', A_2', B_2', C_2', D_2', E_2', G', H', I', J') → P_2, a', j', k', l', m', n', o', p', q', r', s', b', t', u', v', w', y', z', a_1', b_1', c_1', d_1', c', e_1', f_1', g_1', h_1', i_1', j_1', k_1', l_1', m_1', n_1', d', o_1', p_1', q_1', r_1', s_1', t_1', u_1', v_1', w_1', y_1', e', z_1', a_2', b_2', c_2', d_2', e_2', f', g', h', i'
  58. Rotate(A', α, A) → A''
  59. Rotate(B', α, A) → B''
  60. Rotate(C', α, A) → C''
  61. Rotate(D', α, A) → D''
  62. Rotate(E', α, A) → E''
  63. Rotate(F', α, A) → F''
  64. Rotate(G', α, A) → G''
  65. Rotate(H', α, A) → H''
  66. Rotate(I', α, A) → I''
  67. Rotate(J', α, A) → J''
  68. Rotate(K', α, A) → K''
  69. Rotate(L', α, A) → L''
  70. Rotate(M', α, A) → M''
  71. Rotate(N', α, A) → N''
  72. Rotate(O', α, A) → O''
  73. Rotate(P', α, A) → P''
  74. Rotate(Q', α, A) → Q''
  75. Rotate(R', α, A) → R''
  76. Rotate(S', α, A) → S''
  77. Rotate(T', α, A) → T''
  78. Rotate(U', α, A) → U''
  79. Rotate(V', α, A) → V''
  80. Rotate(W', α, A) → W''
  81. Rotate(Y', α, A) → Y''
  82. Rotate(Z', α, A) → Z''
  83. Rotate(A_1', α, A) → A_1''
  84. Rotate(B_1', α, A) → B_1''
  85. Rotate(C_1', α, A) → C_1''
  86. Rotate(D_1', α, A) → D_1''
  87. Rotate(E_1', α, A) → E_1''
  88. Rotate(F_1', α, A) → F_1''
  89. Rotate(G_1', α, A) → G_1''
  90. Rotate(H_1', α, A) → H_1''
  91. Rotate(I_1', α, A) → I_1''
  92. Rotate(J_1', α, A) → J_1''
  93. Rotate(K_1', α, A) → K_1''
  94. Rotate(L_1', α, A) → L_1''
  95. Rotate(M_1', α, A) → M_1''
  96. Rotate(N_1', α, A) → N_1''
  97. Rotate(O_1', α, A) → O_1''
  98. Rotate(P_1', α, A) → P_1''
  99. Rotate(Q_1', α, A) → Q_1''
  100. Rotate(R_1', α, A) → R_1''
  101. Rotate(S_1', α, A) → S_1''
  102. Rotate(T_1', α, A) → T_1''
  103. Rotate(U_1', α, A) → U_1''
  104. Rotate(V_1', α, A) → V_1''
  105. Rotate(W_1', α, A) → W_1''
  106. Rotate(Y_1', α, A) → Y_1''
  107. Rotate(Z_1', α, A) → Z_1''
  108. Rotate(A_2', α, A) → A_2''
  109. Rotate(B_2', α, A) → B_2''
  110. Rotate(C_2', α, A) → C_2''
  111. Rotate(D_2', α, A) → D_2''
  112. Rotate(E_2', α, A) → E_2''
  113. Polygon(A'', B'', K'', L'', M'', N'', O'', P'', Q'', R'', S'', T'', C'', U'', V'', W'', Y'', Z'', A_1'', B_1'', C_1'', D_1'', E_1'', D'', F_1'', G_1'', H_1'', I_1'', J_1'', K_1'', L_1'', M_1'', N_1'', O_1'', E'', P_1'', Q_1'', R_1'', S_1'', T_1'', U_1'', V_1'', W_1'', Y_1'', Z_1'', F'', A_2'', B_2'', C_2'', D_2'', E_2'', G'', H'', I'', J'') → P_3, a'', j'', k'', l'', m'', n'', o'', p'', q'', r'', s'', b'', t'', u'', v'', w'', y'', z'', a_1'', b_1'', c_1'', d_1'', c'', e_1'', f_1'', g_1'', h_1'', i_1'', j_1'', k_1'', l_1'', m_1'', n_1'', d'', o_1'', p_1'', q_1'', r_1'', s_1'', t_1'', u_1'', v_1'', w_1'', y_1'', e'', z_1'', a_2'', b_2'', c_2'', d_2'', e_2'', f'', g'', h'', i''
  114. Vector(Y'', Y) → u
  115. Translate(A, Vector[(a_2 * u)]) → A'_1
  116. Translate(B, Vector[(a_2 * u)]) → B'_1
  117. Translate(C, Vector[(a_2 * u)]) → C'_1
  118. Translate(D, Vector[(a_2 * u)]) → D'_1
  119. Translate(E, Vector[(a_2 * u)]) → E'_1
  120. Translate(F, Vector[(a_2 * u)]) → F'_1
  121. Translate(G, Vector[(a_2 * u)]) → G'_1
  122. Translate(H, Vector[(a_2 * u)]) → H'_1
  123. Translate(I, Vector[(a_2 * u)]) → I'_1
  124. Translate(J, Vector[(a_2 * u)]) → J'_1
  125. Translate(K, Vector[(a_2 * u)]) → K'_1
  126. Translate(L, Vector[(a_2 * u)]) → L'_1
  127. Translate(M, Vector[(a_2 * u)]) → M'_1
  128. Translate(N, Vector[(a_2 * u)]) → N'_1
  129. Translate(O, Vector[(a_2 * u)]) → O'_1
  130. Translate(P, Vector[(a_2 * u)]) → P'_1
  131. Translate(Q, Vector[(a_2 * u)]) → Q'_1
  132. Translate(R, Vector[(a_2 * u)]) → R'_1
  133. Translate(S, Vector[(a_2 * u)]) → S'_1
  134. Translate(T, Vector[(a_2 * u)]) → T'_1
  135. Translate(U, Vector[(a_2 * u)]) → U'_1
  136. Translate(V, Vector[(a_2 * u)]) → V'_1
  137. Translate(W, Vector[(a_2 * u)]) → W'_1
  138. Translate(Y, Vector[(a_2 * u)]) → Y'_1
  139. Translate(Z, Vector[(a_2 * u)]) → Z'_1
  140. Translate(A_1, Vector[(a_2 * u)]) → A_3
  141. Translate(B_1, Vector[(a_2 * u)]) → B_3
  142. Translate(C_1, Vector[(a_2 * u)]) → C_3
  143. Translate(D_1, Vector[(a_2 * u)]) → D_3
  144. Translate(E_1, Vector[(a_2 * u)]) → E_3
  145. Translate(F_1, Vector[(a_2 * u)]) → F_2
  146. Translate(G_1, Vector[(a_2 * u)]) → G_2
  147. Translate(H_1, Vector[(a_2 * u)]) → H_2
  148. Translate(I_1, Vector[(a_2 * u)]) → I_2
  149. Translate(J_1, Vector[(a_2 * u)]) → J_2
  150. Translate(K_1, Vector[(a_2 * u)]) → K_2
  151. Translate(L_1, Vector[(a_2 * u)]) → L_2
  152. Translate(M_1, Vector[(a_2 * u)]) → M_2
  153. Translate(N_1, Vector[(a_2 * u)]) → N_2
  154. Translate(O_1, Vector[(a_2 * u)]) → O_2
  155. Translate(P_4, Vector[(a_2 * u)]) → P_4'
  156. Translate(Q_1, Vector[(a_2 * u)]) → Q_2
  157. Translate(R_1, Vector[(a_2 * u)]) → R_2
  158. Translate(S_1, Vector[(a_2 * u)]) → S_2
  159. Translate(T_1, Vector[(a_2 * u)]) → T_2
  160. Translate(U_1, Vector[(a_2 * u)]) → U_2
  161. Translate(V_1, Vector[(a_2 * u)]) → V_2
  162. Translate(W_1, Vector[(a_2 * u)]) → W_2
  163. Translate(Y_1, Vector[(a_2 * u)]) → Y_3
  164. Translate(Z_1, Vector[(a_2 * u)]) → Z_3
  165. Translate(A_2, Vector[(a_2 * u)]) → A_4
  166. Translate(B_2, Vector[(a_2 * u)]) → B_4
  167. Translate(C_2, Vector[(a_2 * u)]) → C_4
  168. Translate(D_2, Vector[(a_2 * u)]) → D_4
  169. Translate(E_2, Vector[(a_2 * u)]) → E_4
  170. Polygon(A'_1, B'_1, K'_1, L'_1, M'_1, N'_1, O'_1, P'_1, Q'_1, R'_1, S'_1, T'_1, C'_1, U'_1, V'_1, W'_1, Y'_1, Z'_1, A_3, B_3, C_3, D_3, E_3, D'_1, F_2, G_2, H_2, I_2, J_2, K_2, L_2, M_2, N_2, O_2, E'_1, P_4', Q_2, R_2, S_2, T_2, U_2, V_2, W_2, Y_3, Z_3, F'_1, A_4, B_4, C_4, D_4, E_4, G'_1, H'_1, I'_1, J'_1) → P_5, a'_1, j'_1, k'_1, l'_1, m'_1, n'_1, o'_1, p'_1, q'_1, r'_1, s'_1, b'_1, t'_1, u'_1, v'_1, w'_1, y'_1, z'_1, a_3, b_3, c_3, d_3, c'_1, e_3, f_3, g_3, h_3, i_3, j_3, k_3, l_3, m_3, n_3, d'_1, o_2, p_4', q_3, r_3, s_3, t_2, u_2, v_2, w_2, y_3, e'_1, z_3, a_4, b_5, c_4, d_4, e_4, f'_1, g'_1, h'_1, i'_1
  171. Translate(A', Vector[(a_2 * u)]) → A''_1
  172. Translate(B', Vector[(a_2 * u)]) → B''_1
  173. Translate(C', Vector[(a_2 * u)]) → C''_1
  174. Translate(D', Vector[(a_2 * u)]) → D''_1
  175. Translate(E', Vector[(a_2 * u)]) → E''_1
  176. Translate(F', Vector[(a_2 * u)]) → F''_1
  177. Translate(G', Vector[(a_2 * u)]) → G''_1
  178. Translate(H', Vector[(a_2 * u)]) → H''_1
  179. Translate(I', Vector[(a_2 * u)]) → I''_1
  180. Translate(J', Vector[(a_2 * u)]) → J''_1
  181. Translate(K', Vector[(a_2 * u)]) → K''_1
  182. Translate(L', Vector[(a_2 * u)]) → L''_1
  183. Translate(M', Vector[(a_2 * u)]) → M''_1
  184. Translate(N', Vector[(a_2 * u)]) → N''_1
  185. Translate(O', Vector[(a_2 * u)]) → O''_1
  186. Translate(P', Vector[(a_2 * u)]) → P''_1
  187. Translate(Q', Vector[(a_2 * u)]) → Q''_1
  188. Translate(R', Vector[(a_2 * u)]) → R''_1
  189. Translate(S', Vector[(a_2 * u)]) → S''_1
  190. Translate(T', Vector[(a_2 * u)]) → T''_1
  191. Translate(U', Vector[(a_2 * u)]) → U''_1
  192. Translate(V', Vector[(a_2 * u)]) → V''_1
  193. Translate(W', Vector[(a_2 * u)]) → W''_1
  194. Translate(Y', Vector[(a_2 * u)]) → Y''_1
  195. Translate(Z', Vector[(a_2 * u)]) → Z''_1
  196. Translate(A_1', Vector[(a_2 * u)]) → A_5
  197. Translate(B_1', Vector[(a_2 * u)]) → B_5
  198. Translate(C_1', Vector[(a_2 * u)]) → C_5
  199. Translate(D_1', Vector[(a_2 * u)]) → D_5
  200. Translate(E_1', Vector[(a_2 * u)]) → E_5
  201. Translate(F_1', Vector[(a_2 * u)]) → F_3
  202. Translate(G_1', Vector[(a_2 * u)]) → G_3
  203. Translate(H_1', Vector[(a_2 * u)]) → H_3
  204. Translate(I_1', Vector[(a_2 * u)]) → I_3
  205. Translate(J_1', Vector[(a_2 * u)]) → J_3
  206. Translate(K_1', Vector[(a_2 * u)]) → K_3
  207. Translate(L_1', Vector[(a_2 * u)]) → L_3
  208. Translate(M_1', Vector[(a_2 * u)]) → M_3
  209. Translate(N_1', Vector[(a_2 * u)]) → N_3
  210. Translate(O_1', Vector[(a_2 * u)]) → O_3
  211. Translate(P_1', Vector[(a_2 * u)]) → P_6
  212. Translate(Q_1', Vector[(a_2 * u)]) → Q_3
  213. Translate(R_1', Vector[(a_2 * u)]) → R_3
  214. Translate(S_1', Vector[(a_2 * u)]) → S_3
  215. Translate(T_1', Vector[(a_2 * u)]) → T_3
  216. Translate(U_1', Vector[(a_2 * u)]) → U_3
  217. Translate(V_1', Vector[(a_2 * u)]) → V_3
  218. Translate(W_1', Vector[(a_2 * u)]) → W_3
  219. Translate(Y_1', Vector[(a_2 * u)]) → Y_4
  220. Translate(Z_1', Vector[(a_2 * u)]) → Z_4
  221. Translate(A_2', Vector[(a_2 * u)]) → A_6
  222. Translate(B_2', Vector[(a_2 * u)]) → B_6
  223. Translate(C_2', Vector[(a_2 * u)]) → C_6
  224. Translate(D_2', Vector[(a_2 * u)]) → D_6
  225. Translate(E_2', Vector[(a_2 * u)]) → E_6
  226. Polygon(A''_1, B''_1, K''_1, L''_1, M''_1, N''_1, O''_1, P''_1, Q''_1, R''_1, S''_1, T''_1, C''_1, U''_1, V''_1, W''_1, Y''_1, Z''_1, A_5, B_5, C_5, D_5, E_5, D''_1, F_3, G_3, H_3, I_3, J_3, K_3, L_3, M_3, N_3, O_3, E''_1, P_6, Q_3, R_3, S_3, T_3, U_3, V_3, W_3, Y_4, Z_4, F''_1, A_6, B_6, C_6, D_6, E_6, G''_1, H''_1, I''_1, J''_1) → P_2', a''_1, j''_1, k''_1, l''_1, m''_1, n''_1, o''_1, p''_1, q''_1, r''_1, s''_1, b''_1, t''_1, u''_1, v''_1, w''_1, y''_1, z''_1, a_5, b_6, c_5, d_5, c''_1, e_5, f_4, g_4, h_4, i_4, j_4, k_4, l_4, m_4, n_4, d''_1, o_3, p_6, q_4, r_4, s_4, t_3, u_3, v_3, w_3, y_4, e''_1, z_4, a_6, b_7, c_6, d_6, e_6, f''_1, g''_1, h''_1, i''_1
  227. Translate(A'', Vector[(a_2 * u)]) → A'''
  228. Translate(B'', Vector[(a_2 * u)]) → B'''
  229. Translate(C'', Vector[(a_2 * u)]) → C'''
  230. Translate(D'', Vector[(a_2 * u)]) → D'''
  231. Translate(E'', Vector[(a_2 * u)]) → E'''
  232. Translate(F'', Vector[(a_2 * u)]) → F'''
  233. Translate(G'', Vector[(a_2 * u)]) → G'''
  234. Translate(H'', Vector[(a_2 * u)]) → H'''
  235. Translate(I'', Vector[(a_2 * u)]) → I'''
  236. Translate(J'', Vector[(a_2 * u)]) → J'''
  237. Translate(K'', Vector[(a_2 * u)]) → K'''
  238. Translate(L'', Vector[(a_2 * u)]) → L'''
  239. Translate(M'', Vector[(a_2 * u)]) → M'''
  240. Translate(N'', Vector[(a_2 * u)]) → N'''
  241. Translate(O'', Vector[(a_2 * u)]) → O'''
  242. Translate(P'', Vector[(a_2 * u)]) → P'''
  243. Translate(Q'', Vector[(a_2 * u)]) → Q'''
  244. Translate(R'', Vector[(a_2 * u)]) → R'''
  245. Translate(S'', Vector[(a_2 * u)]) → S'''
  246. Translate(T'', Vector[(a_2 * u)]) → T'''
  247. Translate(U'', Vector[(a_2 * u)]) → U'''
  248. Translate(V'', Vector[(a_2 * u)]) → V'''
  249. Translate(W'', Vector[(a_2 * u)]) → W'''
  250. Translate(Y'', Vector[(a_2 * u)]) → Y'''
  251. Translate(Z'', Vector[(a_2 * u)]) → Z'''
  252. Translate(A_1'', Vector[(a_2 * u)]) → A_1'''
  253. Translate(B_1'', Vector[(a_2 * u)]) → B_1'''
  254. Translate(C_1'', Vector[(a_2 * u)]) → C_1'''
  255. Translate(D_1'', Vector[(a_2 * u)]) → D_1'''
  256. Translate(E_1'', Vector[(a_2 * u)]) → E_1'''
  257. Translate(F_1'', Vector[(a_2 * u)]) → F_1'''
  258. Translate(G_1'', Vector[(a_2 * u)]) → G_1'''
  259. Translate(H_1'', Vector[(a_2 * u)]) → H_1'''
  260. Translate(I_1'', Vector[(a_2 * u)]) → I_1'''
  261. Translate(J_1'', Vector[(a_2 * u)]) → J_1'''
  262. Translate(K_1'', Vector[(a_2 * u)]) → K_1'''
  263. Translate(L_1'', Vector[(a_2 * u)]) → L_1'''
  264. Translate(M_1'', Vector[(a_2 * u)]) → M_1'''
  265. Translate(N_1'', Vector[(a_2 * u)]) → N_1'''
  266. Translate(O_1'', Vector[(a_2 * u)]) → O_1'''
  267. Translate(P_1'', Vector[(a_2 * u)]) → P_1'''
  268. Translate(Q_1'', Vector[(a_2 * u)]) → Q_1'''
  269. Translate(R_1'', Vector[(a_2 * u)]) → R_1'''
  270. Translate(S_1'', Vector[(a_2 * u)]) → S_1'''
  271. Translate(T_1'', Vector[(a_2 * u)]) → T_1'''
  272. Translate(U_1'', Vector[(a_2 * u)]) → U_1'''
  273. Translate(V_1'', Vector[(a_2 * u)]) → V_1'''
  274. Translate(W_1'', Vector[(a_2 * u)]) → W_1'''
  275. Translate(Y_1'', Vector[(a_2 * u)]) → Y_1'''
  276. Translate(Z_1'', Vector[(a_2 * u)]) → Z_1'''
  277. Translate(A_2'', Vector[(a_2 * u)]) → A_2'''
  278. Translate(B_2'', Vector[(a_2 * u)]) → B_2'''
  279. Translate(C_2'', Vector[(a_2 * u)]) → C_2'''
  280. Translate(D_2'', Vector[(a_2 * u)]) → D_2'''
  281. Translate(E_2'', Vector[(a_2 * u)]) → E_2'''
  282. Polygon(A''', B''', K''', L''', M''', N''', O''', P''', Q''', R''', S''', T''', C''', U''', V''', W''', Y''', Z''', A_1''', B_1''', C_1''', D_1''', E_1''', D''', F_1''', G_1''', H_1''', I_1''', J_1''', K_1''', L_1''', M_1''', N_1''', O_1''', E''', P_1''', Q_1''', R_1''', S_1''', T_1''', U_1''', V_1''', W_1''', Y_1''', Z_1''', F''', A_2''', B_2''', C_2''', D_2''', E_2''', G''', H''', I''', J''') → P_3', a''', j''', k''', l''', m''', n''', o''', p''', q''', r''', s''', b''', t''', u''', v''', w''', y''', z''', a_1''', b_1''', c_1''', d_1''', c''', e_1''', f_1''', g_1''', h_1''', i_1''', j_1''', k_1''', l_1''', m_1''', n_1''', d''', o_1''', p_1''', q_1''', r_1''', s_1''', t_1''', u_1''', v_1''', w_1''', y_1''', e''', z_1''', a_2''', b_2''', c_2''', d_2''', e_2''', f''', g''', h''', i'''
  283. Vector(Y', Y) → v
  284. Translate(A, Vector[(b_4 * v)]) → A'_2
  285. Translate(B, Vector[(b_4 * v)]) → B'_2
  286. Translate(C, Vector[(b_4 * v)]) → C'_2
  287. Translate(D, Vector[(b_4 * v)]) → D'_2
  288. Translate(E, Vector[(b_4 * v)]) → E'_2
  289. Translate(F, Vector[(b_4 * v)]) → F'_2
  290. Translate(G, Vector[(b_4 * v)]) → G'_2
  291. Translate(H, Vector[(b_4 * v)]) → H'_2
  292. Translate(I, Vector[(b_4 * v)]) → I'_2
  293. Translate(J, Vector[(b_4 * v)]) → J'_2
  294. Translate(K, Vector[(b_4 * v)]) → K'_2
  295. Translate(L, Vector[(b_4 * v)]) → L'_2
  296. Translate(M, Vector[(b_4 * v)]) → M'_2
  297. Translate(N, Vector[(b_4 * v)]) → N'_2
  298. Translate(O, Vector[(b_4 * v)]) → O'_2
  299. Translate(P, Vector[(b_4 * v)]) → P'_2
  300. Translate(Q, Vector[(b_4 * v)]) → Q'_2
  301. Translate(R, Vector[(b_4 * v)]) → R'_2
  302. Translate(S, Vector[(b_4 * v)]) → S'_2
  303. Translate(T, Vector[(b_4 * v)]) → T'_2
  304. Translate(U, Vector[(b_4 * v)]) → U'_2
  305. Translate(V, Vector[(b_4 * v)]) → V'_2
  306. Translate(W, Vector[(b_4 * v)]) → W'_2
  307. Translate(Y, Vector[(b_4 * v)]) → Y'_2
  308. Translate(Z, Vector[(b_4 * v)]) → Z'_2
  309. Translate(A_1, Vector[(b_4 * v)]) → A_7
  310. Translate(B_1, Vector[(b_4 * v)]) → B_7
  311. Translate(C_1, Vector[(b_4 * v)]) → C_7
  312. Translate(D_1, Vector[(b_4 * v)]) → D_7
  313. Translate(E_1, Vector[(b_4 * v)]) → E_7
  314. Translate(F_1, Vector[(b_4 * v)]) → F_4
  315. Translate(G_1, Vector[(b_4 * v)]) → G_4
  316. Translate(H_1, Vector[(b_4 * v)]) → H_4
  317. Translate(I_1, Vector[(b_4 * v)]) → I_4
  318. Translate(J_1, Vector[(b_4 * v)]) → J_4
  319. Translate(K_1, Vector[(b_4 * v)]) → K_4
  320. Translate(L_1, Vector[(b_4 * v)]) → L_4
  321. Translate(M_1, Vector[(b_4 * v)]) → M_4
  322. Translate(N_1, Vector[(b_4 * v)]) → N_4
  323. Translate(O_1, Vector[(b_4 * v)]) → O_4
  324. Translate(P_4, Vector[(b_4 * v)]) → P_7
  325. Translate(Q_1, Vector[(b_4 * v)]) → Q_4
  326. Translate(R_1, Vector[(b_4 * v)]) → R_4
  327. Translate(S_1, Vector[(b_4 * v)]) → S_4
  328. Translate(T_1, Vector[(b_4 * v)]) → T_4
  329. Translate(U_1, Vector[(b_4 * v)]) → U_4
  330. Translate(V_1, Vector[(b_4 * v)]) → V_4
  331. Translate(W_1, Vector[(b_4 * v)]) → W_4
  332. Translate(Y_1, Vector[(b_4 * v)]) → Y_5
  333. Translate(Z_1, Vector[(b_4 * v)]) → Z_5
  334. Translate(A_2, Vector[(b_4 * v)]) → A_8
  335. Translate(B_2, Vector[(b_4 * v)]) → B_8
  336. Translate(C_2, Vector[(b_4 * v)]) → C_8
  337. Translate(D_2, Vector[(b_4 * v)]) → D_8
  338. Translate(E_2, Vector[(b_4 * v)]) → E_8
  339. Polygon(A'_2, B'_2, K'_2, L'_2, M'_2, N'_2, O'_2, P'_2, Q'_2, R'_2, S'_2, T'_2, C'_2, U'_2, V'_2, W'_2, Y'_2, Z'_2, A_7, B_7, C_7, D_7, E_7, D'_2, F_4, G_4, H_4, I_4, J_4, K_4, L_4, M_4, N_4, O_4, E'_2, P_7, Q_4, R_4, S_4, T_4, U_4, V_4, W_4, Y_5, Z_5, F'_2, A_8, B_8, C_8, D_8, E_8, G'_2, H'_2, I'_2, J'_2) → P_8, a'_2, j'_2, k'_2, l'_2, m'_2, n'_2, o'_2, p'_2, q'_2, r'_2, s'_2, b'_2, t'_2, u'_2, v'_2, w'_2, y'_2, z'_2, a_7, b_8, c_7, d_7, c'_2, e_7, f_5, g_5, h_5, i_5, j_5, k_5, l_5, m_5, n_5, d'_2, o_4, p_7, q_5, r_5, s_5, t_4, u_4, v_4, w_4, y_5, e'_2, z_5, a_8, b_9, c_8, d_8, e_8, f'_2, g'_2, h'_2, i'_2
  340. Translate(A', Vector[(b_4 * v)]) → A''_2
  341. Translate(B', Vector[(b_4 * v)]) → B''_2
  342. Translate(C', Vector[(b_4 * v)]) → C''_2
  343. Translate(D', Vector[(b_4 * v)]) → D''_2
  344. Translate(E', Vector[(b_4 * v)]) → E''_2
  345. Translate(F', Vector[(b_4 * v)]) → F''_2
  346. Translate(G', Vector[(b_4 * v)]) → G''_2
  347. Translate(H', Vector[(b_4 * v)]) → H''_2
  348. Translate(I', Vector[(b_4 * v)]) → I''_2
  349. Translate(J', Vector[(b_4 * v)]) → J''_2
  350. Translate(K', Vector[(b_4 * v)]) → K''_2
  351. Translate(L', Vector[(b_4 * v)]) → L''_2
  352. Translate(M', Vector[(b_4 * v)]) → M''_2
  353. Translate(N', Vector[(b_4 * v)]) → N''_2
  354. Translate(O', Vector[(b_4 * v)]) → O''_2
  355. Translate(P', Vector[(b_4 * v)]) → P''_2
  356. Translate(Q', Vector[(b_4 * v)]) → Q''_2
  357. Translate(R', Vector[(b_4 * v)]) → R''_2
  358. Translate(S', Vector[(b_4 * v)]) → S''_2
  359. Translate(T', Vector[(b_4 * v)]) → T''_2
  360. Translate(U', Vector[(b_4 * v)]) → U''_2
  361. Translate(V', Vector[(b_4 * v)]) → V''_2
  362. Translate(W', Vector[(b_4 * v)]) → W''_2
  363. Translate(Y', Vector[(b_4 * v)]) → Y''_2
  364. Translate(Z', Vector[(b_4 * v)]) → Z''_2
  365. Translate(A_1', Vector[(b_4 * v)]) → A_9
  366. Translate(B_1', Vector[(b_4 * v)]) → B_9
  367. Translate(C_1', Vector[(b_4 * v)]) → C_9
  368. Translate(D_1', Vector[(b_4 * v)]) → D_9
  369. Translate(E_1', Vector[(b_4 * v)]) → E_9
  370. Translate(F_1', Vector[(b_4 * v)]) → F_5
  371. Translate(G_1', Vector[(b_4 * v)]) → G_5
  372. Translate(H_1', Vector[(b_4 * v)]) → H_5
  373. Translate(I_1', Vector[(b_4 * v)]) → I_5
  374. Translate(J_1', Vector[(b_4 * v)]) → J_5
  375. Translate(K_1', Vector[(b_4 * v)]) → K_5
  376. Translate(L_1', Vector[(b_4 * v)]) → L_5
  377. Translate(M_1', Vector[(b_4 * v)]) → M_5
  378. Translate(N_1', Vector[(b_4 * v)]) → N_5
  379. Translate(O_1', Vector[(b_4 * v)]) → O_5
  380. Translate(P_1', Vector[(b_4 * v)]) → P_9
  381. Translate(Q_1', Vector[(b_4 * v)]) → Q_5
  382. Translate(R_1', Vector[(b_4 * v)]) → R_5
  383. Translate(S_1', Vector[(b_4 * v)]) → S_5
  384. Translate(T_1', Vector[(b_4 * v)]) → T_5
  385. Translate(U_1', Vector[(b_4 * v)]) → U_5
  386. Translate(V_1', Vector[(b_4 * v)]) → V_5
  387. Translate(W_1', Vector[(b_4 * v)]) → W_5
  388. Translate(Y_1', Vector[(b_4 * v)]) → Y_6
  389. Translate(Z_1', Vector[(b_4 * v)]) → Z_6
  390. Translate(A_2', Vector[(b_4 * v)]) → A_{10}
  391. Translate(B_2', Vector[(b_4 * v)]) → B_{10}
  392. Translate(C_2', Vector[(b_4 * v)]) → C_{10}
  393. Translate(D_2', Vector[(b_4 * v)]) → D_{10}
  394. Translate(E_2', Vector[(b_4 * v)]) → E_{10}
  395. Polygon(A''_2, B''_2, K''_2, L''_2, M''_2, N''_2, O''_2, P''_2, Q''_2, R''_2, S''_2, T''_2, C''_2, U''_2, V''_2, W''_2, Y''_2, Z''_2, A_9, B_9, C_9, D_9, E_9, D''_2, F_5, G_5, H_5, I_5, J_5, K_5, L_5, M_5, N_5, O_5, E''_2, P_9, Q_5, R_5, S_5, T_5, U_5, V_5, W_5, Y_6, Z_6, F''_2, A_{10}, B_{10}, C_{10}, D_{10}, E_{10}, G''_2, H''_2, I''_2, J''_2) → P_{10}, a''_2, j''_2, k''_2, l''_2, m''_2, n''_2, o''_2, p''_2, q''_2, r''_2, s''_2, b''_2, t''_2, u''_2, v''_2, w''_2, y''_2, z''_2, a_9, b_{10}, c_9, d_9, c''_2, e_9, f_6, g_6, h_6, i_6, j_6, k_6, l_6, m_6, n_6, d''_2, o_5, p_9, q_6, r_6, s_6, t_5, u_5, v_5, w_5, y_6, e''_2, z_6, a_{10}, b_{11}, c_{10}, d_{10}, e_{10}, f''_2, g''_2, h''_2, i''_2
  396. Translate(A'', Vector[(b_4 * v)]) → A'''_1
  397. Translate(B'', Vector[(b_4 * v)]) → B'''_1
  398. Translate(C'', Vector[(b_4 * v)]) → C'''_1
  399. Translate(D'', Vector[(b_4 * v)]) → D'''_1
  400. Translate(E'', Vector[(b_4 * v)]) → E'''_1
  401. Translate(F'', Vector[(b_4 * v)]) → F'''_1
  402. Translate(G'', Vector[(b_4 * v)]) → G'''_1
  403. Translate(H'', Vector[(b_4 * v)]) → H'''_1
  404. Translate(I'', Vector[(b_4 * v)]) → I'''_1
  405. Translate(J'', Vector[(b_4 * v)]) → J'''_1
  406. Translate(K'', Vector[(b_4 * v)]) → K'''_1
  407. Translate(L'', Vector[(b_4 * v)]) → L'''_1
  408. Translate(M'', Vector[(b_4 * v)]) → M'''_1
  409. Translate(N'', Vector[(b_4 * v)]) → N'''_1
  410. Translate(O'', Vector[(b_4 * v)]) → O'''_1
  411. Translate(P'', Vector[(b_4 * v)]) → P'''_1
  412. Translate(Q'', Vector[(b_4 * v)]) → Q'''_1
  413. Translate(R'', Vector[(b_4 * v)]) → R'''_1
  414. Translate(S'', Vector[(b_4 * v)]) → S'''_1
  415. Translate(T'', Vector[(b_4 * v)]) → T'''_1
  416. Translate(U'', Vector[(b_4 * v)]) → U'''_1
  417. Translate(V'', Vector[(b_4 * v)]) → V'''_1
  418. Translate(W'', Vector[(b_4 * v)]) → W'''_1
  419. Translate(Y'', Vector[(b_4 * v)]) → Y'''_1
  420. Translate(Z'', Vector[(b_4 * v)]) → Z'''_1
  421. Translate(A_1'', Vector[(b_4 * v)]) → A_{11}
  422. Translate(B_1'', Vector[(b_4 * v)]) → B_{11}
  423. Translate(C_1'', Vector[(b_4 * v)]) → C_{11}
  424. Translate(D_1'', Vector[(b_4 * v)]) → D_{11}
  425. Translate(E_1'', Vector[(b_4 * v)]) → E_{11}
  426. Translate(F_1'', Vector[(b_4 * v)]) → F_6
  427. Translate(G_1'', Vector[(b_4 * v)]) → G_6
  428. Translate(H_1'', Vector[(b_4 * v)]) → H_6
  429. Translate(I_1'', Vector[(b_4 * v)]) → I_6
  430. Translate(J_1'', Vector[(b_4 * v)]) → J_6
  431. Translate(K_1'', Vector[(b_4 * v)]) → K_6
  432. Translate(L_1'', Vector[(b_4 * v)]) → L_6
  433. Translate(M_1'', Vector[(b_4 * v)]) → M_6
  434. Translate(N_1'', Vector[(b_4 * v)]) → N_6
  435. Translate(O_1'', Vector[(b_4 * v)]) → O_6
  436. Translate(P_1'', Vector[(b_4 * v)]) → P_{11}
  437. Translate(Q_1'', Vector[(b_4 * v)]) → Q_6
  438. Translate(R_1'', Vector[(b_4 * v)]) → R_6
  439. Translate(S_1'', Vector[(b_4 * v)]) → S_6
  440. Translate(T_1'', Vector[(b_4 * v)]) → T_6
  441. Translate(U_1'', Vector[(b_4 * v)]) → U_6
  442. Translate(V_1'', Vector[(b_4 * v)]) → V_6
  443. Translate(W_1'', Vector[(b_4 * v)]) → W_6
  444. Translate(Y_1'', Vector[(b_4 * v)]) → Y_7
  445. Translate(Z_1'', Vector[(b_4 * v)]) → Z_7
  446. Translate(A_2'', Vector[(b_4 * v)]) → A_{12}
  447. Translate(B_2'', Vector[(b_4 * v)]) → B_{12}
  448. Translate(C_2'', Vector[(b_4 * v)]) → C_{12}
  449. Translate(D_2'', Vector[(b_4 * v)]) → D_{12}
  450. Translate(E_2'', Vector[(b_4 * v)]) → E_{12}
  451. Polygon(A'''_1, B'''_1, K'''_1, L'''_1, M'''_1, N'''_1, O'''_1, P'''_1, Q'''_1, R'''_1, S'''_1, T'''_1, C'''_1, U'''_1, V'''_1, W'''_1, Y'''_1, Z'''_1, A_{11}, B_{11}, C_{11}, D_{11}, E_{11}, D'''_1, F_6, G_6, H_6, I_6, J_6, K_6, L_6, M_6, N_6, O_6, E'''_1, P_{11}, Q_6, R_6, S_6, T_6, U_6, V_6, W_6, Y_7, Z_7, F'''_1, A_{12}, B_{12}, C_{12}, D_{12}, E_{12}, G'''_1, H'''_1, I'''_1, J'''_1) → P_{12}, a'''_1, j'''_1, k'''_1, l'''_1, m'''_1, n'''_1, o'''_1, p'''_1, q'''_1, r'''_1, s'''_1, b'''_1, t'''_1, u'''_1, v'''_1, w'''_1, y'''_1, z'''_1, a_{11}, b_{12}, c_{11}, d_{11}, c'''_1, e_{11}, f_7, g_7, h_7, i_7, j_7, k_7, l_7, m_7, n_7, d'''_1, o_6, p_{11}, q_7, r_7, s_7, t_6, u_6, v_6, w_6, y_7, e'''_1, z_7, a_{12}, b_{13}, c_{12}, d_{12}, e_{12}, f'''_1, g'''_1, h'''_1, i'''_1

AI Drawing Prompt Reference

Draw an Escher-like polygon tiling pattern, featuring multiple repeated tessellations constructed through rotation and translation. The pattern includes multiple polygons, including an initial polygon and its rotated and translated copies. Each polygon has multiple vertices, with specific relationships and connections between them. The construction sequence starts with creating the initial polygon, followed by creating its copies through rotation and translation, and finally connecting the vertices to form the tessellations.
The prompt above was compiled from the original drawing commands and is for reference only.