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Translation Tessellation 8

Translation Tessellation 8
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2013-07-20 05:26
PolygonTransformationGeometric Construction
In collections Translation Tessellation
This example demonstrates the application of translation in polygon tessellation. Key mathematical concepts include translation, polygons, and similarity transformations. Using GeoGebra commands such as Polygon, Segment, and Translate, the construction of translated polygons is illustrated. Suitable for middle school and above students learning geometric transformations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 6) → poly1, a, F, b, c, d, e, f, C, D, E
  2. Segment(C, G) → g
  3. Segment(G, H) → h
  4. Segment(H, I) → i
  5. Segment(I, J) → j
  6. Segment(J, K) → k
  7. Segment(K, L) → l
  8. Segment(L, M) → m
  9. Segment(M, N) → n
  10. LineBisector(c) → p
  11. Segment(N, O) → q
  12. Segment(O, P) → r
  13. Segment(P, Q) → s
  14. Segment(Q, R) → t
  15. Point(p) → S
  16. Segment(R, S) → a_1
  17. Mirror(C, p) → C'
  18. Mirror(G, p) → G'
  19. Segment(C', G') → g'
  20. Mirror(G, p) → G'_1
  21. Mirror(H, p) → H'
  22. Segment(G'_1, H') → h'
  23. Mirror(H, p) → H'_1
  24. Mirror(I, p) → I'
  25. Segment(H'_1, I') → i'
  26. Mirror(I, p) → I'_1
  27. Mirror(J, p) → J'
  28. Segment(I'_1, J') → j'
  29. Mirror(J, p) → J'_1
  30. Mirror(K, p) → K'
  31. Segment(J'_1, K') → k'
  32. Mirror(K, p) → K'_1
  33. Mirror(L, p) → L'
  34. Segment(K'_1, L') → l'
  35. Mirror(L, p) → L'_1
  36. Mirror(M, p) → M'
  37. Segment(L'_1, M') → m'
  38. Mirror(M, p) → M'_1
  39. Mirror(N, p) → N'
  40. Segment(M'_1, N') → n'
  41. Mirror(N, p) → N'_1
  42. Mirror(O, p) → O'
  43. Segment(N'_1, O') → q'
  44. Mirror(O, p) → O'_1
  45. Mirror(P, p) → P'
  46. Segment(O'_1, P') → r'
  47. Mirror(P, p) → P'_1
  48. Mirror(Q, p) → Q'
  49. Segment(P'_1, Q') → s'
  50. Mirror(Q, p) → Q'_1
  51. Mirror(R, p) → R'
  52. Segment(Q'_1, R') → t'
  53. Mirror(R, p) → R'_1
  54. Mirror(S, p) → S'
  55. Segment(R'_1, S') → b_1
  56. Vector(C, A) → u
  57. Translate(C, u) → C'_1
  58. Translate(D, u) → D'
  59. Translate(C, u) → C'_2
  60. Translate(G, u) → G'_2
  61. Segment(C'_2, G'_2) → g'_1
  62. Translate(G, u) → G'_3
  63. Translate(H, u) → H'_2
  64. Segment(G'_3, H'_2) → h'_1
  65. Translate(H, u) → H'_3
  66. Translate(I, u) → I'_2
  67. Segment(H'_3, I'_2) → i'_1
  68. Translate(I, u) → I'_3
  69. Translate(J, u) → J'_2
  70. Segment(I'_3, J'_2) → j'_1
  71. Translate(J, u) → J'_3
  72. Translate(K, u) → K'_2
  73. Segment(J'_3, K'_2) → k'_1
  74. Translate(K, u) → K'_3
  75. Translate(L, u) → L'_2
  76. Segment(K'_3, L'_2) → l'_1
  77. Translate(L, u) → L'_3
  78. Translate(M, u) → M'_2
  79. Segment(L'_3, M'_2) → m'_1
  80. Translate(M, u) → M'_3
  81. Translate(N, u) → N'_2
  82. Segment(M'_3, N'_2) → n'_1
  83. Translate(N, u) → N'_3
  84. Translate(O, u) → O'_2
  85. Segment(N'_3, O'_2) → q'_1
  86. Translate(O, u) → O'_3
  87. Translate(P, u) → P'_2
  88. Segment(O'_3, P'_2) → r'_1
  89. Translate(P, u) → P'_3
  90. Translate(Q, u) → Q'_2
  91. Segment(P'_3, Q'_2) → s'_1
  92. Translate(Q, u) → Q'_3
  93. Translate(R, u) → R'_2
  94. Segment(Q'_3, R'_2) → t'_1
  95. Translate(R, u) → R'_3
  96. Translate(S, u) → S'_1
  97. Segment(R'_3, S'_1) → c_1
  98. Translate(C', u) → C''
  99. Translate(G', u) → G''
  100. Segment(C'', G'') → g''
  101. Translate(G'_1, u) → T
  102. Translate(H', u) → H''
  103. Segment(T, H'') → h''
  104. Translate(H'_1, u) → U
  105. Translate(I', u) → I''
  106. Segment(U, I'') → i''
  107. Translate(I'_1, u) → V
  108. Translate(J', u) → J''
  109. Segment(V, J'') → j''
  110. Translate(J'_1, u) → W
  111. Translate(K', u) → K''
  112. Segment(W, K'') → k''
  113. Translate(K'_1, u) → Z
  114. Translate(L', u) → L''
  115. Segment(Z, L'') → l''
  116. Translate(L'_1, u) → A_1
  117. Translate(M', u) → M''
  118. Segment(A_1, M'') → m''
  119. Translate(M'_1, u) → B_1
  120. Translate(N', u) → N''
  121. Segment(B_1, N'') → n''
  122. Translate(N'_1, u) → C_1
  123. Translate(O', u) → O''
  124. Segment(C_1, O'') → q''
  125. Translate(O'_1, u) → D_1
  126. Translate(P', u) → P''
  127. Segment(D_1, P'') → r''
  128. Translate(P'_1, u) → E_1
  129. Translate(Q', u) → Q''
  130. Segment(E_1, Q'') → s''
  131. Translate(Q'_1, u) → F_1
  132. Translate(R', u) → R''
  133. Segment(F_1, R'') → t''
  134. Translate(R'_1, u) → G_1
  135. Translate(S', u) → S''
  136. Segment(G_1, S'') → d_1
  137. Segment(B, H_1) → e_1
  138. Segment(H_1, I_1) → f_1
  139. Segment(I_1, J_1) → g_1
  140. Segment(J_1, K_1) → h_1
  141. Segment(K_1, L_1) → i_1
  142. Segment(L_1, M_1) → j_1
  143. Segment(M_1, N_1) → k_1
  144. Segment(N_1, O_1) → l_1
  145. Segment(O_1, P_1) → m_1
  146. Segment(P_1, Q_1) → n_1
  147. Segment(Q_1, C) → p_1
  148. Vector(B, F) → v
  149. Translate(B, v) → B'
  150. Translate(C, v) → C'_3
  151. Translate(B, v) → B'_1
  152. Translate(H_1, v) → R_1
  153. Segment(B'_1, R_1) → q_1
  154. Translate(H_1, v) → S_1
  155. Translate(I_1, v) → T_1
  156. Segment(S_1, T_1) → r_1
  157. Translate(I_1, v) → U_1
  158. Translate(J_1, v) → V_1
  159. Segment(U_1, V_1) → s_1
  160. Translate(J_1, v) → W_1
  161. Translate(K_1, v) → Z_1
  162. Segment(W_1, Z_1) → t_1
  163. Translate(K_1, v) → A_2
  164. Translate(L_1, v) → B_2
  165. Segment(A_2, B_2) → a_2
  166. Translate(L_1, v) → C_2
  167. Translate(M_1, v) → D_2
  168. Segment(C_2, D_2) → b_2
  169. Translate(M_1, v) → E_2
  170. Translate(N_1, v) → F_2
  171. Segment(E_2, F_2) → c_2
  172. Translate(N_1, v) → G_2
  173. Translate(O_1, v) → H_2
  174. Segment(G_2, H_2) → d_2
  175. Translate(O_1, v) → I_2
  176. Translate(P_1, v) → J_2
  177. Segment(I_2, J_2) → e_2
  178. Translate(P_1, v) → K_2
  179. Translate(Q_1, v) → L_2
  180. Segment(K_2, L_2) → f_2
  181. Translate(Q_1, v) → M_2
  182. Translate(C, v) → C'_4
  183. Segment(M_2, C'_4) → g_2
  184. Mirror(B, p) → B'_2
  185. Mirror(C, p) → C'_5
  186. Mirror(B, p) → B'_3
  187. Mirror(H_1, p) → N_2
  188. Segment(B'_3, N_2) → h_2
  189. Mirror(H_1, p) → O_2
  190. Mirror(I_1, p) → P_2
  191. Segment(O_2, P_2) → i_2
  192. Mirror(I_1, p) → Q_2
  193. Mirror(J_1, p) → R_2
  194. Segment(Q_2, R_2) → j_2
  195. Mirror(J_1, p) → S_2
  196. Mirror(K_1, p) → T_2
  197. Segment(S_2, T_2) → k_2
  198. Mirror(K_1, p) → U_2
  199. Mirror(L_1, p) → V_2
  200. Segment(U_2, V_2) → l_2
  201. Mirror(L_1, p) → W_2
  202. Mirror(M_1, p) → Z_2
  203. Segment(W_2, Z_2) → m_2
  204. Mirror(M_1, p) → A_3
  205. Mirror(N_1, p) → B_3
  206. Segment(A_3, B_3) → n_2
  207. Mirror(N_1, p) → C_3
  208. Mirror(O_1, p) → D_3
  209. Segment(C_3, D_3) → p_2
  210. Mirror(O_1, p) → E_3
  211. Mirror(P_1, p) → F_3
  212. Segment(E_3, F_3) → q_2
  213. Mirror(P_1, p) → G_3
  214. Mirror(Q_1, p) → H_3
  215. Segment(G_3, H_3) → r_2
  216. Mirror(Q_1, p) → I_3
  217. Mirror(C, p) → C'_6
  218. Segment(I_3, C'_6) → s_2
  219. Vector(E, A) → w
  220. Translate(D, w) → D'_1
  221. Translate(E, w) → E'
  222. Translate(B'_2, w) → J_3
  223. Translate(C'_5, w) → K_3
  224. Translate(B'_3, w) → L_3
  225. Translate(N_2, w) → M_3
  226. Segment(L_3, M_3) → a_3
  227. Translate(O_2, w) → N_3
  228. Translate(P_2, w) → O_3
  229. Segment(N_3, O_3) → b_3
  230. Translate(Q_2, w) → P_3
  231. Translate(R_2, w) → Q_3
  232. Segment(P_3, Q_3) → c_3
  233. Translate(S_2, w) → R_3
  234. Translate(T_2, w) → S_3
  235. Segment(R_3, S_3) → d_3
  236. Translate(U_2, w) → T_3
  237. Translate(V_2, w) → U_3
  238. Segment(T_3, U_3) → e_3
  239. Translate(W_2, w) → V_3
  240. Translate(Z_2, w) → W_3
  241. Segment(V_3, W_3) → f_3
  242. Translate(A_3, w) → Z_3
  243. Translate(B_3, w) → A_4
  244. Segment(Z_3, A_4) → g_3
  245. Translate(C_3, w) → B_4
  246. Translate(D_3, w) → C_4
  247. Segment(B_4, C_4) → h_3
  248. Translate(E_3, w) → D_4
  249. Translate(F_3, w) → E_4
  250. Segment(D_4, E_4) → i_3
  251. Translate(G_3, w) → F_4
  252. Translate(H_3, w) → G_4
  253. Segment(F_4, G_4) → j_3
  254. Translate(I_3, w) → H_4
  255. Translate(C'_6, w) → I_4
  256. Segment(H_4, I_4) → k_3
  257. Translate(C', w) → C''_1
  258. Translate(C'_3, w) → J_4
  259. Translate(C'_4, w) → K_4
  260. Polygon(S'_1, R'', I'', H'', G'', F, R_1, T_1, V_1, Z_1, B_2, D_2, Q'', F_2, H_2, J_2, L_2, E, N_2, P_2, R_2, T_2, V_2, P'', Z_2, B_3, D_3, F_3, H_3, D, G', H', I', J', O'', K', L', M', N', O', P', Q', R', S, R, N'', Q, P, O, N, M, L, K, J, I, H, M'', G, C, Q_1, P_1, O_1, N_1, M_1, L_1, K_1, J_1, L'', I_1, H_1, B, G_4, E_4, C_4, A_4, W_3, U_3, S_3, K'', Q_3, O_3, M_3, A, G'_2, H'_2, I'_2, J'_2, K'_2, L'_2, J'', M'_2, N'_2, O'_2, P'_2, Q'_2, R'_2) → poly2, s'_2, j''_1, i''_1, h''_1, g''_1, f_4, r_3, t_2, v_1, z_1, b_4, r''_1, d_4, f_5, h_4, j_4, l_3, e_4, n_3, p_3, r_4, t_3, q''_1, v_2, z_2, b_5, d_5, f_6, h_5, d_6, g'_2, h'_2, i'_2, p'', j'_2, k'_2, l'_2, m'_2, n'_2, o', p', q'_2, r'_2, s_3, o'', r_5, q_3, p_4, o, n_4, m_3, l_4, k_4, j_5, i_4, n''_1, h_6, g_4, c_4, q_4, p_5, o_1, n_5, m_4, l_5, k_5, m''_1, j_6, i_5, h_7, b_6, g_5, e_5, c_5, a_4, w_3, u_3, l''_1, s_4, q_5, o_3, m_5, a_5, g'_3, h'_3, i'_3, j'_3, k'_3, k''_1, l'_3, m'_3, n'_3, o'_2, p'_2, q'_3, r'_3

AI Drawing Prompt Reference

Draw a hexagon and connect its vertices to form segments. Then, use the perpendicular bisectors of these segments as axes to mirror and flip the hexagon, creating a pattern composed of multiple hexagons.
The prompt above was compiled from the original drawing commands and is for reference only.