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Convex Hexagon Tessellations

Convex Hexagon Tessellations
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2014-09-16 21:46
Polygon
This example demonstrates the construction and observation of convex hexagon tessellations using GeoGebra. Key mathematical concepts include polygons, geometric transformations (rotation, translation), vectors, and angles. The construction involves commands and objects such as Segment, Line, Circle, Intersect, Polygon, Midpoint, Rotate, Vector, Translate, Point, Angle, Ray, AngularBisector, Mirror, and TableText. It is suitable for high school and above students to understand the application of geometric transformations in plane tessellations and their aesthetic properties.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Line(D, a) → b_2
  3. Circle(D, a) → c_2
  4. Intersect(c_2, b_2, 1) → E
  5. Segment(B, C) → b
  6. Segment(C, D) → c
  7. Segment(D, E) → d
  8. Segment(E, F) → e
  9. Segment(F, A) → f
  10. Polygon(A, B, C, D, E, F) → poly1, a_1, b_1, c_1, d_1, e_1, f_1
  11. Midpoint(D, C) → G
  12. Rotate(A, 3.141592653589793, G) → A'
  13. Rotate(B, 3.141592653589793, G) → B'
  14. Rotate(C, 3.141592653589793, G) → C'
  15. Rotate(D, 3.141592653589793, G) → D'
  16. Rotate(E, 3.141592653589793, G) → E'
  17. Rotate(F, 3.141592653589793, G) → F'
  18. Polygon(A', B', C', D', E', F') → poly1', a', b', c', d', e', f'
  19. Vector(B', D') → u
  20. Translate(A', u) → A''
  21. Translate(B', u) → B''
  22. Translate(C', u) → C''
  23. Translate(D', u) → D''
  24. Translate(E', u) → E''
  25. Translate(F', u) → F''
  26. Polygon(A'', B'', C'', D'', E'', F'') → poly1'', a'', b'', c'', d'', e'', f''
  27. Translate(A'', u) → A'''
  28. Translate(B'', u) → B'''
  29. Translate(C'', u) → C'''
  30. Translate(D'', u) → D'''
  31. Translate(E'', u) → E'''
  32. Translate(F'', u) → F'''
  33. Polygon(A''', B''', C''', D''', E''', F''') → poly1''', a''', b''', c''', d''', e''', f'''
  34. Translate(A, u) → A'_1
  35. Translate(B, u) → B'_1
  36. Translate(C, u) → C'_1
  37. Translate(D, u) → D'_1
  38. Translate(E, u) → E'_1
  39. Translate(F, u) → F'_1
  40. Polygon(A'_1, B'_1, C'_1, D'_1, E'_1, F'_1) → poly1'_1, a'_1, b'_1, c'_1, d'_1, e'_1, f'_1
  41. Translate(A'_1, u) → A'_1'
  42. Translate(B'_1, u) → B'_1'
  43. Translate(C'_1, u) → C'_1'
  44. Translate(D'_1, u) → D'_1'
  45. Translate(E'_1, u) → E'_1'
  46. Translate(F'_1, u) → F'_1'
  47. Polygon(A'_1', B'_1', C'_1', D'_1', E'_1', F'_1') → poly1'_1', a'_1', b'_1', c'_1', d'_1', e'_1', f'_1'
  48. Vector(F, A'') → v
  49. Translate(A, v) → A'_2
  50. Translate(B, v) → B'_2
  51. Translate(C, v) → C'_2
  52. Translate(D, v) → D'_2
  53. Translate(E, v) → E'_2
  54. Translate(F, v) → F'_2
  55. Polygon(A'_2, B'_2, C'_2, D'_2, E'_2, F'_2) → poly1'_2, a'_2, b'_2, c'_2, d'_2, e'_2, f'_2
  56. Translate(A'_1, v) → A'_3
  57. Translate(B'_1, v) → B'_3
  58. Translate(C'_1, v) → C'_3
  59. Translate(D'_1, v) → D'_3
  60. Translate(E'_1, v) → E'_3
  61. Translate(F'_1, v) → F'_3
  62. Polygon(A'_3, B'_3, C'_3, D'_3, E'_3, F'_3) → poly1'_3, a'_3, b'_3, c'_3, d'_3, e'_3, f'_3
  63. Translate(A'_1', v) → A'_1''
  64. Translate(B'_1', v) → B'_1''
  65. Translate(C'_1', v) → C'_1''
  66. Translate(D'_1', v) → D'_1''
  67. Translate(E'_1', v) → E'_1''
  68. Translate(F'_1', v) → F'_1''
  69. Polygon(A'_1'', B'_1'', C'_1'', D'_1'', E'_1'', F'_1'') → poly1'_1'', a'_1'', b'_1'', c'_1'', d'_1'', e'_1'', f'_1''
  70. Translate(A', v) → A''_1
  71. Translate(B', v) → B''_1
  72. Translate(C', v) → C''_1
  73. Translate(D', v) → D''_1
  74. Translate(E', v) → E''_1
  75. Translate(F', v) → F''_1
  76. Polygon(A''_1, B''_1, C''_1, D''_1, E''_1, F''_1) → poly1''_1, a''_1, b''_1, c''_1, d''_1, e''_1, f''_1
  77. Translate(A'', v) → A'''_1
  78. Translate(B'', v) → B'''_1
  79. Translate(C'', v) → C'''_1
  80. Translate(D'', v) → D'''_1
  81. Translate(E'', v) → E'''_1
  82. Translate(F'', v) → F'''_1
  83. Polygon(A'''_1, B'''_1, C'''_1, D'''_1, E'''_1, F'''_1) → poly1'''_1, a'''_1, b'''_1, c'''_1, d'''_1, e'''_1, f'''_1
  84. Translate(A''', v) → A''''
  85. Translate(B''', v) → B''''
  86. Translate(C''', v) → C''''
  87. Translate(D''', v) → D''''
  88. Translate(E''', v) → E''''
  89. Translate(F''', v) → F''''
  90. Polygon(A'''', B'''', C'''', D'''', E'''', F'''') → poly1'''', a'''', b'''', c'''', d'''', e'''', f''''
  91. Translate(A'_1', u) → A'_4
  92. Translate(B'_1', u) → B'_4
  93. Translate(C'_1', u) → C'_4
  94. Translate(D'_1', u) → D'_4
  95. Translate(E'_1', u) → E'_4
  96. Translate(F'_1', u) → F'_4
  97. Polygon(A'_4, B'_4, C'_4, D'_4, E'_4, F'_4) → poly1'_4, a'_4, b'_4, c'_4, d'_4, e'_4, f'_4
  98. Translate(A''', u) → A''''_1
  99. Translate(B''', u) → B''''_1
  100. Translate(C''', u) → C''''_1
  101. Translate(D''', u) → D''''_1
  102. Translate(E''', u) → E''''_1
  103. Translate(F''', u) → F''''_1
  104. Polygon(A''''_1, B''''_1, C''''_1, D''''_1, E''''_1, F''''_1) → poly1''''_1, a''''_1, b''''_1, c''''_1, d''''_1, e''''_1, f''''_1
  105. Translate(A'_1'', u) → A'_1'''
  106. Translate(B'_1'', u) → B'_1'''
  107. Translate(C'_1'', u) → C'_1'''
  108. Translate(D'_1'', u) → D'_1'''
  109. Translate(E'_1'', u) → E'_1'''
  110. Translate(F'_1'', u) → F'_1'''
  111. Polygon(A'_1''', B'_1''', C'_1''', D'_1''', E'_1''', F'_1''') → poly1'_1''', a'_1''', b'_1''', c'_1''', d'_1''', e'_1''', f'_1'''
  112. Translate(A'''', u) → A'''''
  113. Translate(B'''', u) → B'''''
  114. Translate(C'''', u) → C'''''
  115. Translate(D'''', u) → D'''''
  116. Translate(E'''', u) → E'''''
  117. Translate(F'''', u) → F'''''
  118. Polygon(A''''', B''''', C''''', D''''', E''''', F''''') → poly1''''', a''''', b''''', c''''', d''''', e''''', f'''''
  119. Segment(A_1, B_1) → b_3
  120. Segment(F_1, A_1) → a_2
  121. Segment(B_1, C_1) → c_3
  122. Circle(C_1, a_2) → cir_1
  123. Point(cir_1) → D_1
  124. Segment(C_1, D_1) → d_2
  125. Angle(B_1, A_1, F_1) → α_1
  126. Angle(C_1, B_1, A_1) → β_1
  127. Rotate(C_1, (-((2 * 3.141592653589793) - α_1 - β_1)), D_1) → C'_5
  128. Angle(C'_5, D_1, C_1) → γ_1
  129. Ray(D_1, C'_5) → e_2
  130. Circle(D_1, c_3) → f_2
  131. Intersect(f_2, e_2, 1) → E_1
  132. Segment(D_1, E_1) → e_3
  133. Segment(E_1, F_1) → f_3
  134. Midpoint(b_3) → G_1
  135. Polygon(A_1, B_1, C_1, D_1, E_1, F_1) → poly1_1, a_3, b_4, c_4, d_3, e_4, f_4
  136. Rotate(A_1, 180°, G_1) → A'_5
  137. Rotate(B_1, 180°, G_1) → B'_5
  138. Rotate(C_1, 180°, G_1) → C'_6
  139. Rotate(D_1, 180°, G_1) → D'_5
  140. Rotate(E_1, 180°, G_1) → E'_5
  141. Rotate(F_1, 180°, G_1) → F'_5
  142. Polygon(A'_5, B'_5, C'_6, D'_5, E'_5, F'_5) → poly1'_5, a'_5, b'_5, c'_5, d'_5, e'_5, f'_5
  143. Line(C_1, a_2) → g_1
  144. AngularBisector(g_1, d_2) → h_1, i_1
  145. Mirror(A_1, h_1) → A'_6
  146. Mirror(B_1, h_1) → B'_6
  147. Mirror(C_1, h_1) → C'_7
  148. Mirror(D_1, h_1) → D'_6
  149. Mirror(E_1, h_1) → E'_6
  150. Mirror(F_1, h_1) → F'_6
  151. Polygon(A'_6, B'_6, C'_7, D'_6, E'_6, F'_6) → poly1'_6, a'_6, b'_6, c'_6, d'_6, e'_6, f'_6
  152. Vector(C_1, F_1) → u_1
  153. Translate(A'_6, u_1) → H_1
  154. Translate(B'_6, u_1) → I_1
  155. Translate(C'_7, u_1) → J_1
  156. Translate(D'_6, u_1) → K_1
  157. Translate(E'_6, u_1) → L_1
  158. Translate(F'_6, u_1) → M_1
  159. Polygon(H_1, I_1, J_1, K_1, L_1, M_1) → poly2_1, h_2, i_2, j_1, k_1, l_1, m_1
  160. Rotate(H_1, 180°, G_1) → H'_1
  161. Rotate(I_1, 180°, G_1) → I'_1
  162. Rotate(J_1, 180°, G_1) → J'_1
  163. Rotate(K_1, 180°, G_1) → K'_1
  164. Rotate(L_1, 180°, G_1) → L'_1
  165. Rotate(M_1, 180°, G_1) → M'_1
  166. Polygon(H'_1, I'_1, J'_1, K'_1, L'_1, M'_1) → poly2'_1, h'_1, i'_1, j'_1, k'_1, l'_1, m'_1
  167. Vector(E_1, F'_5) → v_1
  168. Translate(A_1, v_1) → A'_7
  169. Translate(B_1, v_1) → B'_7
  170. Translate(C_1, v_1) → C'_8
  171. Translate(D_1, v_1) → D'_7
  172. Translate(E_1, v_1) → E'_7
  173. Translate(F_1, v_1) → F'_7
  174. Polygon(A'_7, B'_7, C'_8, D'_7, E'_7, F'_7) → poly1'_7, a'_7, b'_7, c'_7, d'_7, e'_7, f'_7
  175. Translate(H'_1, v_1) → H''_1
  176. Translate(I'_1, v_1) → I''_1
  177. Translate(J'_1, v_1) → J''_1
  178. Translate(K'_1, v_1) → K''_1
  179. Translate(L'_1, v_1) → L''_1
  180. Translate(M'_1, v_1) → M''_1
  181. Polygon(H''_1, I''_1, J''_1, K''_1, L''_1, M''_1) → poly2''_1, h''_1, i''_1, j''_1, k''_1, l''_1, m''_1
  182. Translate(A'_5, v_1) → A''_2
  183. Translate(B'_5, v_1) → B''_2
  184. Translate(C'_6, v_1) → N_1
  185. Translate(D'_5, v_1) → D''_2
  186. Translate(E'_5, v_1) → E''_2
  187. Translate(F'_5, v_1) → F''_2
  188. Polygon(A''_2, B''_2, N_1, D''_2, E''_2, F''_2) → poly1''_2, a''_2, b''_2, n_1, d''_2, e''_2, f''_2
  189. Translate(H_1, v_1) → H'_2
  190. Translate(I_1, v_1) → I'_2
  191. Translate(J_1, v_1) → J'_2
  192. Translate(K_1, v_1) → K'_2
  193. Translate(L_1, v_1) → L'_2
  194. Translate(M_1, v_1) → M'_2
  195. Polygon(H'_2, I'_2, J'_2, K'_2, L'_2, M'_2) → poly2'_2, h'_2, i'_2, j'_2, k'_2, l'_2, m'_2
  196. Vector(M'_1, C'_6) → w_1
  197. Translate(H'_1, w_1) → H''_2
  198. Translate(I'_1, w_1) → I''_2
  199. Translate(J'_1, w_1) → J''_2
  200. Translate(K'_1, w_1) → K''_2
  201. Translate(L'_1, w_1) → L''_2
  202. Translate(M'_1, w_1) → M''_2
  203. Polygon(H''_2, I''_2, J''_2, K''_2, L''_2, M''_2) → poly2''_2, h''_2, i''_2, j''_2, k''_2, l''_2, m''_2
  204. Translate(A_1, w_1) → A'_8
  205. Translate(B_1, w_1) → B'_8
  206. Translate(C_1, w_1) → C'_9
  207. Translate(D_1, w_1) → D'_8
  208. Translate(E_1, w_1) → E'_8
  209. Translate(F_1, w_1) → F'_8
  210. Polygon(A'_8, B'_8, C'_9, D'_8, E'_8, F'_8) → poly1'_8, a'_8, b'_8, c'_8, d'_8, e'_8, f'_8
  211. Translate(A'_7, w_1) → O_1
  212. Translate(B'_7, w_1) → P_1
  213. Translate(C'_8, w_1) → Q_1
  214. Translate(D'_7, w_1) → R_1
  215. Translate(E'_7, w_1) → S_1
  216. Translate(F'_7, w_1) → T_1
  217. Polygon(O_1, P_1, Q_1, R_1, S_1, T_1) → poly3_1, o_1, p_1, q_1, r_1, s_1, t_1
  218. Translate(H''_1, w_1) → H'''_1
  219. Translate(I''_1, w_1) → I'''_1
  220. Translate(J''_1, w_1) → J'''_1
  221. Translate(K''_1, w_1) → K'''_1
  222. Translate(L''_1, w_1) → L'''_1
  223. Translate(M''_1, w_1) → M'''_1
  224. Polygon(H'''_1, I'''_1, J'''_1, K'''_1, L'''_1, M'''_1) → poly2'''_1, h'''_1, i'''_1, j'''_1, k'''_1, l'''_1, m'''_1
  225. Translate(A'_5, w_1) → A''_3
  226. Translate(B'_5, w_1) → B''_3
  227. Translate(C'_6, w_1) → U_1
  228. Translate(D'_5, w_1) → D''_3
  229. Translate(E'_5, w_1) → E''_3
  230. Translate(F'_5, w_1) → F''_3
  231. Polygon(A''_3, B''_3, U_1, D''_3, E''_3, F''_3) → poly1''_3, a''_3, b''_3, u_2, d''_3, e''_3, f''_3
  232. Translate(H_1, w_1) → H'_3
  233. Translate(I_1, w_1) → I'_3
  234. Translate(J_1, w_1) → J'_3
  235. Translate(K_1, w_1) → K'_3
  236. Translate(L_1, w_1) → L'_3
  237. Translate(M_1, w_1) → M'_3
  238. Polygon(H'_3, I'_3, J'_3, K'_3, L'_3, M'_3) → poly2'_3, h'_3, i'_3, j'_3, k'_3, l'_3, m'_3
  239. Translate(A''_2, w_1) → A'''_2
  240. Translate(B''_2, w_1) → B'''_2
  241. Translate(N_1, w_1) → N'_1
  242. Translate(D''_2, w_1) → D'''_2
  243. Translate(E''_2, w_1) → E'''_2
  244. Translate(F''_2, w_1) → F'''_2
  245. Polygon(A'''_2, B'''_2, N'_1, D'''_2, E'''_2, F'''_2) → poly1'''_2, a'''_2, b'''_2, n'_1, d'''_2, e'''_2, f'''_2
  246. Translate(H'_2, w_1) → V_1
  247. Translate(I'_2, w_1) → W_1
  248. Translate(J'_2, w_1) → Z_1
  249. Translate(K'_2, w_1) → A_2
  250. Translate(L'_2, w_1) → B_2
  251. Translate(M'_2, w_1) → C_2
  252. Polygon(V_1, W_1, Z_1, A_2, B_2, C_2) → poly4_1, v_2, w_2, z_1, a_4, b_5, c_5
  253. Segment(A_3, B_3) → a_5
  254. Rotate(B_3, 120°, A_3) → F_2
  255. Segment(B_3, C_3) → c'_9
  256. Segment(A_3, F_2) → a'_9
  257. Rotate(B_3, 240°, C_3) → D_2
  258. Segment(C_3, D_2) → c_6
  259. Midpoint(D_2, F_2) → M_2
  260. Circle(D_2, M_2) → d_4
  261. Circle(M_2, D_2) → e_5
  262. Intersect(d_4, e_5, 2) → E_2
  263. AngularBisector(M_2, D_2, E_2) → b_6
  264. Intersect(e_5, b_6, 2) → G_2
  265. AngularBisector(M_2, F_2, G_2) → f_5
  266. Intersect(b_6, f_5) → E_3
  267. Segment(D_2, E_3) → e'_9
  268. Segment(E_3, F_2) → e_6
  269. Polygon(A_3, B_3, C_3, D_2, E_3, F_2) → poly1_2, a_6, b_7, c_7, d_5, e_7, f_6
  270. Rotate(A_3, 120°, C_3) → A'_9
  271. Rotate(B_3, 120°, C_3) → B'_9
  272. Rotate(C_3, 120°, C_3) → C'_{10}
  273. Rotate(D_2, 120°, C_3) → D'_9
  274. Rotate(E_3, 120°, C_3) → E'_9
  275. Rotate(F_2, 120°, C_3) → F'_9
  276. Polygon(A'_9, B'_9, C'_{10}, D'_9, E'_9, F'_9) → poly1'_9, a'_{10}, b'_9, c'_{10}, d'_9, e'_{10}, f'_9
  277. Rotate(A'_9, 120°, C_3) → A''_4
  278. Rotate(B'_9, 120°, C_3) → B''_4
  279. Rotate(C'_{10}, 120°, C_3) → C''_2
  280. Rotate(D'_9, 120°, C_3) → D''_4
  281. Rotate(E'_9, 120°, C_3) → E''_4
  282. Rotate(F'_9, 120°, C_3) → F''_4
  283. Polygon(A''_4, B''_4, C''_2, D''_4, E''_4, F''_4) → poly1''_4, a''_4, b''_4, c''_2, d''_4, e''_4, f''_4
  284. Vector(A_3, A'_9) → u_3
  285. Translate(A_3, u_3) → A'_{10}
  286. Translate(B_3, u_3) → B'_{10}
  287. Translate(C_3, u_3) → C'_{11}
  288. Translate(D_2, u_3) → D'_{10}
  289. Translate(E_3, u_3) → E'_{10}
  290. Translate(F_2, u_3) → F'_{10}
  291. Polygon(A'_{10}, B'_{10}, C'_{11}, D'_{10}, E'_{10}, F'_{10}) → poly1'_{10}, a'_{11}, b'_{10}, c'_{11}, d'_{10}, e'_{11}, f'_{10}
  292. Translate(A'_9, u_3) → A''_5
  293. Translate(B'_9, u_3) → B''_5
  294. Translate(C'_{10}, u_3) → C''_3
  295. Translate(D'_9, u_3) → D''_5
  296. Translate(E'_9, u_3) → E''_5
  297. Translate(F'_9, u_3) → F''_5
  298. Polygon(A''_5, B''_5, C''_3, D''_5, E''_5, F''_5) → poly1''_5, a''_5, b''_5, c''_3, d''_5, e''_5, f''_5
  299. Translate(A''_4, u_3) → A'''_3
  300. Translate(B''_4, u_3) → B'''_3
  301. Translate(C''_2, u_3) → C'''_2
  302. Translate(D''_4, u_3) → D'''_3
  303. Translate(E''_4, u_3) → E'''_3
  304. Translate(F''_4, u_3) → F'''_3
  305. Polygon(A'''_3, B'''_3, C'''_2, D'''_3, E'''_3, F'''_3) → poly1'''_3, a'''_3, b'''_3, c'''_2, d'''_3, e'''_3, f'''_3
  306. Vector(F''_4, B_3) → v_3
  307. Translate(A''_4, v_3) → A'''_4
  308. Translate(B''_4, v_3) → B'''_4
  309. Translate(C''_2, v_3) → C'''_3
  310. Translate(D''_4, v_3) → D'''_4
  311. Translate(E''_4, v_3) → E'''_4
  312. Translate(F''_4, v_3) → F'''_4
  313. Polygon(A'''_4, B'''_4, C'''_3, D'''_4, E'''_4, F'''_4) → poly1'''_4, a'''_4, b'''_4, c'''_3, d'''_4, e'''_4, f'''_4
  314. Translate(A'_{10}, v_3) → H_2
  315. Translate(B'_{10}, v_3) → I_2
  316. Translate(C'_{11}, v_3) → J_2
  317. Translate(D'_{10}, v_3) → K_2
  318. Translate(E'_{10}, v_3) → L_2
  319. Translate(F'_{10}, v_3) → N_2
  320. Polygon(H_2, I_2, J_2, K_2, L_2, N_2) → poly2_2, h_3, i_3, j_2, k_2, l_2, n_2
  321. Translate(A'''_3, v_3) → O_2
  322. Translate(B'''_3, v_3) → P_2
  323. Translate(C'''_2, v_3) → Q_2
  324. Translate(D'''_3, v_3) → R_2
  325. Translate(E'''_3, v_3) → S_2
  326. Translate(F'''_3, v_3) → T_2
  327. Polygon(O_2, P_2, Q_2, R_2, S_2, T_2) → poly3_2, o_2, p_2, q_2, r_2, s_2, t_2
  328. Translate(A''_5, v_3) → U_2
  329. Translate(B''_5, v_3) → V_2
  330. Translate(C''_3, v_3) → W_2
  331. Translate(D''_5, v_3) → Z_2
  332. Translate(E''_5, v_3) → A_4
  333. Translate(F''_5, v_3) → B_4
  334. Polygon(U_2, V_2, W_2, Z_2, A_4, B_4) → poly4_2, u_4, v_4, w_3, z_2, a_7, b_8
  335. Translate(H_2, u_3) → H'_4
  336. Translate(I_2, u_3) → I'_4
  337. Translate(J_2, u_3) → J'_4
  338. Translate(K_2, u_3) → K'_4
  339. Translate(L_2, u_3) → L'_4
  340. Translate(N_2, u_3) → N'_2
  341. Polygon(H'_4, I'_4, J'_4, K'_4, L'_4, N'_2) → poly2'_4, h'_4, i'_4, j'_4, k'_4, l'_4, n'_2
  342. Translate(O_2, u_3) → O'_1
  343. Translate(P_2, u_3) → P'_1
  344. Translate(Q_2, u_3) → Q'_1
  345. Translate(R_2, u_3) → R'_1
  346. Translate(S_2, u_3) → S'_1
  347. Translate(T_2, u_3) → T'_1
  348. Polygon(O'_1, P'_1, Q'_1, R'_1, S'_1, T'_1) → poly3'_1, o'_1, p'_1, q'_1, r'_1, s'_1, t'_1
  349. Translate(A'_{10}, u_3) → C_4
  350. Translate(B'_{10}, u_3) → D_3
  351. Translate(C'_{11}, u_3) → F_3
  352. Translate(D'_{10}, u_3) → G_3
  353. Translate(E'_{10}, u_3) → H_3
  354. Translate(F'_{10}, u_3) → I_3
  355. Polygon(C_4, D_3, F_3, G_3, H_3, I_3) → poly5_1, c_8, d_6, f_7, g_2, h_4, i_4
  356. Translate(O'_1, v_3) → O''_1
  357. Translate(P'_1, v_3) → P''_1
  358. Translate(Q'_1, v_3) → Q''_1
  359. Translate(R'_1, v_3) → R''_1
  360. Translate(S'_1, v_3) → S''_1
  361. Translate(T'_1, v_3) → T''_1
  362. Polygon(O''_1, P''_1, Q''_1, R''_1, S''_1, T''_1) → poly3''_1, o''_1, p''_1, q''_1, r''_1, s''_1, t''_1
  363. Translate(O_2, v_3) → O'_2
  364. Translate(P_2, v_3) → P'_2
  365. Translate(Q_2, v_3) → Q'_2
  366. Translate(R_2, v_3) → R'_2
  367. Translate(S_2, v_3) → S'_2
  368. Translate(T_2, v_3) → T'_2
  369. Polygon(O'_2, P'_2, Q'_2, R'_2, S'_2, T'_2) → poly3'_2, o'_2, p'_2, q'_2, r'_2, s'_2, t'_2
  370. Translate(A'_9, v_3) → A''_6
  371. Translate(B'_9, v_3) → B''_6
  372. Translate(C'_{10}, v_3) → C''_4
  373. Translate(D'_9, v_3) → D''_6
  374. Translate(E'_9, v_3) → E''_6
  375. Translate(F'_9, v_3) → F''_6
  376. Polygon(A''_6, B''_6, C''_4, D''_6, E''_6, F''_6) → poly1''_6, a''_6, b''_6, c''_4, d''_6, e''_6, f''_6
  377. TableText({Element[list1, type]}, "v") → text3

AI Drawing Prompt Reference

Draw a convex hexagon tessellation by creating a hexagon, rotating it around one vertex to form a new hexagon, and then translating the new hexagon using a vector. Repeat this process by translating the original and new hexagons to create multiple hexagons, demonstrating geometric transformations in plane tessellations.
The prompt above was compiled from the original drawing commands and is for reference only.