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Final Step Tessellation 2

Final Step Tessellation 2
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2014-04-09 04:41
PolygonCoordinate GeometrySolid Geometry
In collections Hexagon- Translation Tessellation (Monster)
This example demonstrates the geometric construction process of tessellations using elements like rhombuses, spheres, and conic sections. Key math concepts include polygon construction, vector operations, transformations, and coordinate geometry. The construction involves commands like Polygon, Segment, Vector, Translate, Circle, and Intersect from GeoGebra, highlighting spatial geometry and transformation principles. Suitable for high school and above learners to understand the principles of spatial geometry and graphical transformations, enhancing geometric construction skills.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 6) → poly1, a, F, b, c, d, e, f, C, D, E
  2. Segment(A, 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, B) → l
  8. Vector(A, E) → u
  9. Translate(A, u) → A'
  10. Translate(B, u) → B'
  11. Segment(A', B') → a'
  12. Translate(A, u) → A'_1
  13. Translate(G, u) → G'
  14. Segment(A'_1, G') → g'
  15. Translate(G, u) → G'_1
  16. Translate(H, u) → H'
  17. Segment(G'_1, H') → h'
  18. Translate(H, u) → H'_1
  19. Translate(I, u) → I'
  20. Segment(H'_1, I') → i'
  21. Translate(I, u) → I'_1
  22. Translate(J, u) → J'
  23. Segment(I'_1, J') → j'
  24. Translate(J, u) → J'_1
  25. Translate(K, u) → K'
  26. Segment(J'_1, K') → k'
  27. Translate(K, u) → K'_1
  28. Translate(B, u) → B'_1
  29. Segment(K'_1, B'_1) → l'
  30. Segment(A, L) → m
  31. Segment(L, M) → n
  32. Segment(M, N) → p
  33. Segment(N, F) → q
  34. Vector(F, D) → v
  35. Translate(F, v) → F'
  36. Translate(A, v) → A'_2
  37. Segment(F', A'_2) → f'
  38. Translate(A, v) → A'_3
  39. Translate(L, v) → L'
  40. Segment(A'_3, L') → m'
  41. Translate(L, v) → L'_1
  42. Translate(M, v) → M'
  43. Segment(L'_1, M') → n'
  44. Translate(M, v) → M'_1
  45. Translate(N, v) → N'
  46. Segment(M'_1, N') → p'
  47. Translate(N, v) → N'_1
  48. Translate(F, v) → F'_1
  49. Segment(N'_1, F'_1) → q'
  50. Segment(B, O) → r
  51. Segment(O, P) → s
  52. Segment(P, Q) → t
  53. Segment(A'_3, Q) → a_1
  54. Vector(B, F) → w
  55. Translate(B, w) → B'_2
  56. Translate(C, w) → C'
  57. Segment(B'_2, C') → b'
  58. Translate(B, w) → B'_3
  59. Translate(O, w) → O'
  60. Segment(B'_3, O') → r'
  61. Translate(O, w) → O'_1
  62. Translate(P, w) → P'
  63. Segment(O'_1, P') → s'
  64. Translate(P, w) → P'_1
  65. Translate(Q, w) → Q'
  66. Segment(P'_1, Q') → t'
  67. Translate(A'_3, w) → R
  68. Translate(Q, w) → Q'_1
  69. Segment(R, Q'_1) → b_1
  70. Vector(F, B) → u_1
  71. Translate(A, u_1) → A'_4
  72. Translate(G, u_1) → G'_2
  73. Segment(A'_4, G'_2) → g'_1
  74. Translate(G, u_1) → G'_3
  75. Translate(H, u_1) → H'_2
  76. Segment(G'_3, H'_2) → h'_1
  77. Translate(H, u_1) → H'_3
  78. Translate(I, u_1) → I'_2
  79. Segment(H'_3, I'_2) → i'_1
  80. Translate(I, u_1) → I'_3
  81. Translate(J, u_1) → J'_2
  82. Segment(I'_3, J'_2) → j'_1
  83. Translate(J, u_1) → J'_3
  84. Translate(K, u_1) → K'_2
  85. Segment(J'_3, K'_2) → k'_1
  86. Translate(K, u_1) → K'_3
  87. Translate(B, u_1) → B'_4
  88. Segment(K'_3, B'_4) → l'_1
  89. Translate(A'_1, u_1) → T
  90. Translate(G', u_1) → G''
  91. Segment(T, G'') → g''
  92. Translate(G'_1, u_1) → U
  93. Translate(H', u_1) → H''
  94. Segment(U, H'') → h''
  95. Translate(H'_1, u_1) → V
  96. Translate(I', u_1) → I''
  97. Segment(V, I'') → i''
  98. Translate(I'_1, u_1) → W
  99. Translate(J', u_1) → J''
  100. Segment(W, J'') → j''
  101. Translate(J'_1, u_1) → Z
  102. Translate(K', u_1) → K''
  103. Segment(Z, K'') → k''
  104. Translate(K'_1, u_1) → A_1
  105. Translate(B'_1, u_1) → B_1
  106. Segment(A_1, B_1) → l''
  107. Translate(A, u_1) → A'_5
  108. Translate(L, u_1) → L'_2
  109. Segment(A'_5, L'_2) → m'_1
  110. Translate(L, u_1) → L'_3
  111. Translate(M, u_1) → M'_2
  112. Segment(L'_3, M'_2) → n'_1
  113. Translate(M, u_1) → M'_3
  114. Translate(N, u_1) → N'_2
  115. Segment(M'_3, N'_2) → p'_1
  116. Translate(N, u_1) → N'_3
  117. Translate(F, u_1) → F'_2
  118. Segment(N'_3, F'_2) → q'_1
  119. Translate(A'_3, u_1) → C_1
  120. Translate(L', u_1) → L''
  121. Segment(C_1, L'') → m''
  122. Translate(L'_1, u_1) → D_1
  123. Translate(M', u_1) → M''
  124. Segment(D_1, M'') → n''
  125. Translate(M'_1, u_1) → E_1
  126. Translate(N', u_1) → N''
  127. Segment(E_1, N'') → p''
  128. Translate(N'_1, u_1) → F_1
  129. Translate(F'_1, u_1) → G_1
  130. Segment(F_1, G_1) → q''
  131. Translate(B, u_1) → B'_5
  132. Translate(O, u_1) → O'_2
  133. Segment(B'_5, O'_2) → r'_1
  134. Translate(O, u_1) → O'_3
  135. Translate(P, u_1) → P'_2
  136. Segment(O'_3, P'_2) → s'_1
  137. Translate(P, u_1) → P'_3
  138. Translate(Q, u_1) → Q'_2
  139. Segment(P'_3, Q'_2) → t'_1
  140. Translate(A'_3, u_1) → H_1
  141. Translate(Q, u_1) → Q'_3
  142. Segment(H_1, Q'_3) → c_1
  143. Translate(B'_3, u_1) → I_1
  144. Translate(O', u_1) → O''
  145. Segment(I_1, O'') → r''
  146. Translate(O'_1, u_1) → J_1
  147. Translate(P', u_1) → P''
  148. Segment(J_1, P'') → s''
  149. Translate(P'_1, u_1) → K_1
  150. Translate(Q', u_1) → Q''
  151. Segment(K_1, Q'') → t''
  152. Translate(R, u_1) → R'
  153. Translate(Q'_1, u_1) → L_1
  154. Segment(R', L_1) → d_1
  155. Translate(D, u_1) → D'
  156. Translate(F', u_1) → F''
  157. Translate(B'_2, u_1) → M_1
  158. Translate(C', u_1) → C''
  159. Segment(N_1, O_1) → e_1
  160. Segment(O_1, P_1) → f_1
  161. Segment(P_1, N_1) → g_1
  162. Segment(Q_1, R_1) → h_1
  163. Segment(R_1, S_1) → i_1
  164. Segment(S_1, Q_1) → j_1
  165. Segment(T_1, U_1) → k_1
  166. Segment(U_1, V_1) → l_1
  167. Segment(V_1, T_1) → m_1
  168. Segment(W_1, Z_1) → n_1
  169. Segment(Z_1, A_2) → p_1
  170. Segment(A_2, W_1) → q_1
  171. Circle(B_2, C_2) → r_1
  172. Circle(B_3, C_3) → r_2
  173. Circle(B_4, C_4) → r_3
  174. Circle(B_5, C_5) → r_4
  175. Polygon(D_2, E_2, F_2) → poly2, f_2, d_2, e_2
  176. Polygon(E_2, H_2, G_2) → poly3, g_2, e_3, h_2
  177. Polygon(G_2, I_2, J_2) → poly4, j_2, g_3, i_2
  178. Polygon(D_3, E_3, F_3) → poly2_1, f_3, d_3, e_4
  179. Polygon(E_3, H_3, G_3) → poly3_1, g_4, e_5, h_3
  180. Polygon(G_3, I_3, J_3) → poly4_1, j_3, g_5, i_3
  181. Intersect(g, h) → K_2
  182. Intersect(g', h') → L_2
  183. Vector(L_2, K_2) → v_1
  184. Translate(D_2, v_1) → M_2
  185. Translate(E_2, v_1) → N_2
  186. Translate(F_2, v_1) → O_2
  187. Polygon(M_2, N_2, O_2) → poly2', o_2, m_2, n_2
  188. Translate(E_2, v_1) → P_2
  189. Translate(H_2, v_1) → Q_2
  190. Translate(G_2, v_1) → R_2
  191. Polygon(P_2, Q_2, R_2) → poly3', r_5, p_2, q_2
  192. Translate(G_2, v_1) → S_2
  193. Translate(I_2, v_1) → T_2
  194. Translate(J_2, v_1) → U_2
  195. Polygon(S_2, T_2, U_2) → poly4', u_2, s_2, t_2
  196. Translate(D_3, v_1) → V_2
  197. Translate(E_3, v_1) → W_2
  198. Translate(F_3, v_1) → Z_2
  199. Polygon(V_2, W_2, Z_2) → poly5, z_2, v_2, w_2
  200. Translate(E_3, v_1) → A_3
  201. Translate(H_3, v_1) → K_3
  202. Translate(G_3, v_1) → L_3
  203. Polygon(A_3, K_3, L_3) → poly6, l_3, a_3, k_3
  204. Translate(G_3, v_1) → M_3
  205. Translate(I_3, v_1) → N_3
  206. Translate(J_3, v_1) → O_3
  207. Polygon(M_3, N_3, O_3) → poly7, o_3, m_3, n_3
  208. Translate(r_1, v_1) → s_1
  209. Translate(r_2, v_1) → t_1
  210. Translate(r_3, v_1) → c_2
  211. Translate(r_4, v_1) → k_2
  212. Translate(A, v_1) → A'_6
  213. Translate(G, v_1) → G'_4
  214. Segment(A'_6, G'_4) → g'_2
  215. Translate(G, v_1) → G'_5
  216. Translate(H, v_1) → H'_4
  217. Segment(G'_5, H'_4) → h'_2
  218. Translate(H, v_1) → H'_5
  219. Translate(I, v_1) → I'_4
  220. Segment(H'_5, I'_4) → i'_2
  221. Translate(I, v_1) → I'_5
  222. Translate(J, v_1) → J'_4
  223. Segment(I'_5, J'_4) → j'_2
  224. Translate(J, v_1) → J'_5
  225. Translate(K, v_1) → K'_4
  226. Segment(J'_5, K'_4) → k'_2
  227. Translate(K, v_1) → K'_5
  228. Translate(B, v_1) → B'_6
  229. Segment(K'_5, B'_6) → l'_2
  230. Translate(A'_1, v_1) → P_3
  231. Translate(G', v_1) → G''_1
  232. Segment(P_3, G''_1) → g''_1
  233. Translate(G'_1, v_1) → Q_3
  234. Translate(H', v_1) → H''_1
  235. Segment(Q_3, H''_1) → h''_1
  236. Translate(H'_1, v_1) → R_3
  237. Translate(I', v_1) → I''_1
  238. Segment(R_3, I''_1) → i''_1
  239. Translate(I'_1, v_1) → S_3
  240. Translate(J', v_1) → J''_1
  241. Segment(S_3, J''_1) → j''_1
  242. Translate(J'_1, v_1) → T_3
  243. Translate(K', v_1) → K''_1
  244. Segment(T_3, K''_1) → k''_1
  245. Translate(K'_1, v_1) → U_3
  246. Translate(B'_1, v_1) → V_3
  247. Segment(U_3, V_3) → l''_1
  248. Translate(A, v_1) → A'_7
  249. Translate(L, v_1) → L'_4
  250. Segment(A'_7, L'_4) → m'_2
  251. Translate(L, v_1) → L'_5
  252. Translate(M, v_1) → M'_4
  253. Segment(L'_5, M'_4) → n'_2
  254. Translate(M, v_1) → M'_5
  255. Translate(N, v_1) → N'_4
  256. Segment(M'_5, N'_4) → p'_2
  257. Translate(N, v_1) → N'_5
  258. Translate(F, v_1) → F'_3
  259. Segment(N'_5, F'_3) → q'_2
  260. Translate(A'_3, v_1) → W_3
  261. Translate(L', v_1) → L''_1
  262. Segment(W_3, L''_1) → m''_1
  263. Translate(L'_1, v_1) → Z_3
  264. Translate(M', v_1) → M''_1
  265. Segment(Z_3, M''_1) → n''_1
  266. Translate(M'_1, v_1) → A_4
  267. Translate(N', v_1) → N''_1
  268. Segment(A_4, N''_1) → p''_1
  269. Translate(N'_1, v_1) → D_4
  270. Translate(F'_1, v_1) → E_4
  271. Segment(D_4, E_4) → q''_1
  272. Translate(B, v_1) → B'_7
  273. Translate(O, v_1) → O'_4
  274. Segment(B'_7, O'_4) → r'_2
  275. Translate(O, v_1) → O'_5
  276. Translate(P, v_1) → P'_4
  277. Segment(O'_5, P'_4) → s'_2
  278. Translate(P, v_1) → P'_5
  279. Translate(Q, v_1) → Q'_4
  280. Segment(P'_5, Q'_4) → t'_2
  281. Translate(A'_3, v_1) → F_4
  282. Translate(Q, v_1) → Q'_5
  283. Segment(F_4, Q'_5) → a_2
  284. Translate(B'_3, v_1) → G_4
  285. Translate(O', v_1) → O''_1
  286. Segment(G_4, O''_1) → r''_1
  287. Translate(O'_1, v_1) → H_4
  288. Translate(P', v_1) → P''_1
  289. Segment(H_4, P''_1) → s''_1
  290. Translate(P'_1, v_1) → I_4
  291. Translate(Q', v_1) → Q''_1
  292. Segment(I_4, Q''_1) → t''_1
  293. Translate(R, v_1) → R'_1
  294. Translate(Q'_1, v_1) → J_4
  295. Segment(R'_1, J_4) → b_2
  296. Translate(A'_4, v_1) → K_4
  297. Translate(G'_2, v_1) → L_4
  298. Segment(K_4, L_4) → l_2
  299. Translate(G'_3, v_1) → M_4
  300. Translate(H'_2, v_1) → N_4
  301. Segment(M_4, N_4) → b_3
  302. Translate(H'_3, v_1) → O_4
  303. Translate(I'_2, v_1) → P_4
  304. Segment(O_4, P_4) → c_3
  305. Translate(I'_3, v_1) → Q_4
  306. Translate(J'_2, v_1) → R_4
  307. Segment(Q_4, R_4) → p_3
  308. Translate(J'_3, v_1) → S_4
  309. Translate(K'_2, v_1) → T_4
  310. Segment(S_4, T_4) → q_3
  311. Translate(K'_3, v_1) → U_4
  312. Translate(B'_4, v_1) → V_4
  313. Segment(U_4, V_4) → s_3
  314. Translate(T, v_1) → T'
  315. Translate(G'', v_1) → G'''
  316. Segment(T', G''') → g'''
  317. Translate(U, v_1) → U'
  318. Translate(H'', v_1) → H'''
  319. Segment(U', H''') → h'''
  320. Translate(V, v_1) → V'
  321. Translate(I'', v_1) → I'''
  322. Segment(V', I''') → i'''
  323. Translate(W, v_1) → W'
  324. Translate(J'', v_1) → J'''
  325. Segment(W', J''') → j'''
  326. Translate(Z, v_1) → Z'
  327. Translate(K'', v_1) → K'''
  328. Segment(Z', K''') → k'''
  329. Translate(A_1, v_1) → W_4
  330. Translate(B_1, v_1) → Z_4
  331. Segment(W_4, Z_4) → l'''
  332. Translate(A'_5, v_1) → A_5
  333. Translate(L'_2, v_1) → D_5
  334. Segment(A_5, D_5) → t_3
  335. Translate(L'_3, v_1) → E_5
  336. Translate(M'_2, v_1) → F_5
  337. Segment(E_5, F_5) → a_4
  338. Translate(M'_3, v_1) → G_5
  339. Translate(N'_2, v_1) → H_5
  340. Segment(G_5, H_5) → b_4
  341. Translate(N'_3, v_1) → I_5
  342. Translate(F'_2, v_1) → J_5
  343. Segment(I_5, J_5) → c_4
  344. Translate(C_1, v_1) → K_5
  345. Translate(L'', v_1) → L'''
  346. Segment(K_5, L''') → m'''
  347. Translate(D_1, v_1) → L_5
  348. Translate(M'', v_1) → M'''
  349. Segment(L_5, M''') → n'''
  350. Translate(E_1, v_1) → M_5
  351. Translate(N'', v_1) → N'''
  352. Segment(M_5, N''') → p'''
  353. Translate(F_1, v_1) → N_5
  354. Translate(G_1, v_1) → O_5
  355. Segment(N_5, O_5) → q'''
  356. Translate(B'_5, v_1) → P_5
  357. Translate(O'_2, v_1) → Q_5
  358. Segment(P_5, Q_5) → d_4
  359. Translate(O'_3, v_1) → R_5
  360. Translate(P'_2, v_1) → S_5
  361. Segment(R_5, S_5) → f_4
  362. Translate(P'_3, v_1) → T_5
  363. Translate(Q'_2, v_1) → U_5
  364. Segment(T_5, U_5) → h_4
  365. Translate(H_1, v_1) → V_5
  366. Translate(Q'_3, v_1) → W_5
  367. Segment(V_5, W_5) → i_4
  368. Translate(I_1, v_1) → Z_5
  369. Translate(O'', v_1) → O'''
  370. Segment(Z_5, O''') → r'''
  371. Translate(J_1, v_1) → A_6
  372. Translate(P'', v_1) → P'''
  373. Segment(A_6, P''') → s'''
  374. Translate(K_1, v_1) → B_6
  375. Translate(Q'', v_1) → Q'''
  376. Segment(B_6, Q''') → t'''
  377. Translate(R', v_1) → R''
  378. Translate(L_1, v_1) → C_6
  379. Segment(R'', C_6) → j_4
  380. Translate(N_1, v_1) → D_6
  381. Translate(O_1, v_1) → E_6
  382. Segment(D_6, E_6) → k_4
  383. Translate(O_1, v_1) → F_6
  384. Translate(P_1, v_1) → G_6
  385. Segment(F_6, G_6) → l_4
  386. Translate(P_1, v_1) → H_6
  387. Translate(N_1, v_1) → I_6
  388. Segment(H_6, I_6) → m_4
  389. Translate(Q_1, v_1) → J_6
  390. Translate(R_1, v_1) → K_6
  391. Segment(J_6, K_6) → n_4
  392. Translate(R_1, v_1) → L_6
  393. Translate(S_1, v_1) → M_6
  394. Segment(L_6, M_6) → p_4
  395. Translate(S_1, v_1) → N_6
  396. Translate(Q_1, v_1) → O_6
  397. Segment(N_6, O_6) → q_4
  398. Translate(T_1, v_1) → P_6
  399. Translate(U_1, v_1) → Q_6
  400. Segment(P_6, Q_6) → s_4
  401. Translate(U_1, v_1) → R_6
  402. Translate(V_1, v_1) → S_6
  403. Segment(R_6, S_6) → t_4
  404. Translate(V_1, v_1) → T_6
  405. Translate(T_1, v_1) → U_6
  406. Segment(T_6, U_6) → a_5
  407. Translate(W_1, v_1) → V_6
  408. Translate(Z_1, v_1) → W_6
  409. Segment(V_6, W_6) → b_5
  410. Translate(Z_1, v_1) → Z_6
  411. Translate(A_2, v_1) → A_7
  412. Segment(Z_6, A_7) → c_5
  413. Translate(A_2, v_1) → B_7
  414. Translate(W_1, v_1) → C_7
  415. Segment(B_7, C_7) → d_5
  416. Translate(B_2, v_1) → D_7
  417. Translate(B_3, v_1) → E_7
  418. Translate(B_4, v_1) → F_7
  419. Translate(B_5, v_1) → G_7

AI Drawing Prompt Reference

Draw a hexagon using points A and B as starting points, completing it with points F, C, D, E, and B. Then, starting from point A, draw vector u towards point E, and translate points A and B along vector u to get A' and B', and connect A' and B'. Repeat this process for points G, H, I, J, and K to form the second hexagon. Finally, starting from point F, draw vector v towards point D, and translate points F and A along vector v to get F' and A'_2, and connect F' and A'_2. Repeat this process for points L, M, N, and F to form the third hexagon.
The prompt above was compiled from the original drawing commands and is for reference only.