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Tessellation from Triangle by abbey (2)

Tessellation from Triangle by abbey (2)
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2013-07-12 06:41
TriangleGeometric Construction
In collections Tessellation from Triangle using Rotation
This example demonstrates how to generate a tessellation pattern by rotating a triangle. Key mathematical concepts include rotation, angles, and geometric construction. It uses commands like Polygon, Segment, Rotate, LineBisector, and Intersect in GeoGebra. Suitable for middle school and above students to learn geometric transformations and tessellations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, a, b, c, C
  2. Segment(B, D) → d
  3. Segment(D, E) → e
  4. Segment(E, F) → f
  5. Segment(F, G) → g
  6. Segment(G, A) → h
  7. Rotate(A, 300*°, B) → A'
  8. Rotate(B, 300*°, B) → B'
  9. Segment(A', B') → a'
  10. Rotate(B, 300*°, B) → B'_1
  11. Rotate(D, 300*°, B) → D'
  12. Segment(B'_1, D') → d'
  13. Rotate(D, 300*°, B) → D'_1
  14. Rotate(E, 300*°, B) → E'
  15. Segment(D'_1, E') → e'
  16. Rotate(E, 300*°, B) → E'_1
  17. Rotate(F, 300*°, B) → F'
  18. Segment(E'_1, F') → f'
  19. Rotate(F, 300*°, B) → F'_1
  20. Rotate(G, 300*°, B) → G'
  21. Segment(F'_1, G') → g'
  22. Rotate(G, 300*°, B) → G'_1
  23. Rotate(A, 300*°, B) → A'_1
  24. Segment(G'_1, A'_1) → h'
  25. LineBisector(c) → i
  26. Intersect(i, c) → H
  27. Point(i) → I
  28. Segment(H, J) → j
  29. Segment(J, K) → k
  30. Segment(K, C) → l
  31. Rotate(G'_1, 180*°, H) → L
  32. Rotate(A'_1, 180*°, H) → M
  33. Rotate(H, 180*°, H) → H'
  34. Rotate(J, 180*°, H) → J'
  35. Segment(H', J') → j'
  36. Rotate(J, 180*°, H) → J'_1
  37. Rotate(K, 180*°, H) → K'
  38. Segment(J'_1, K') → k'
  39. Rotate(K, 180*°, H) → K'_1
  40. Rotate(C, 180*°, H) → C'
  41. Segment(K'_1, C') → l'
  42. Rotate(A', 180*°, H) → A''
  43. Rotate(G', 180*°, H) → G''
  44. Polygon(F', G', E, D, B, D', E', C, K, J, H, K', A, G, F) → poly2, f'_1, f_1, e_1, d_1, b_1, d'_1, e'_1, g'_1, c_1, k_1, j_1, h_1, k'_1, a_1, g_1
  45. Polygon(A, G, C, K, J, H, J', K', F, E, D, B, D', E', F', G') → poly3, a_2, g'_2, c_2, k_2, j_2, h_2, j'_1, k'_2, g_2, f_2, e_2, d_2, b_2, d'_2, e'_2, f'_2
  46. Point(l') → O
  47. Circle(N, O) → p
  48. Segment(P, Q) → m
  49. Segment(S, R) → n
  50. Segment(T, U) → q
  51. Rotate(A, 240*°, A) → A'_2
  52. Rotate(G, 240*°, A) → G'_2
  53. Rotate(F, 240*°, A) → F'_2
  54. Rotate(E, 240*°, A) → E'_2
  55. Rotate(D, 240*°, A) → D'_2
  56. Rotate(B, 240*°, A) → B'_2
  57. Rotate(D', 240*°, A) → D''
  58. Rotate(E', 240*°, A) → E''
  59. Rotate(F', 240*°, A) → F''
  60. Rotate(G', 240*°, A) → G''_1
  61. Rotate(C, 240*°, A) → C'_1
  62. Rotate(K, 240*°, A) → K'_2
  63. Rotate(J, 240*°, A) → J'_2
  64. Rotate(H, 240*°, A) → H'_1
  65. Rotate(J', 240*°, A) → J''
  66. Rotate(K', 240*°, A) → K''
  67. Polygon(A'_2, G'_2, C'_1, K'_2, J'_2, H'_1, J'', K'', F'_2, E'_2, D'_2, B'_2, D'', E'', F'', G''_1) → poly3', a'_2, g''_1, c'_1, k'_3, j'_2, h'_1, j'', k'', g'_3, f'_3, e'_3, d'_3, b'_2, d'', e'', f''
  68. Rotate(p, 240*°, A) → p'
  69. Rotate(B, 240*°, A) → B'_3
  70. Rotate(D, 240*°, A) → D'_3
  71. Segment(B'_3, D'_3) → d'_4
  72. Rotate(D, 240*°, A) → D'_4
  73. Rotate(E, 240*°, A) → E'_3
  74. Segment(D'_4, E'_3) → e'_4
  75. Rotate(E, 240*°, A) → E'_4
  76. Rotate(F, 240*°, A) → F'_3
  77. Segment(E'_4, F'_3) → f'_4
  78. Rotate(F, 240*°, A) → F'_4
  79. Rotate(G, 240*°, A) → G'_3
  80. Segment(F'_4, G'_3) → g'_4
  81. Rotate(G, 240*°, A) → G'_4
  82. Rotate(A, 240*°, A) → A'_3
  83. Segment(G'_4, A'_3) → h'_2
  84. Rotate(B'_1, 240*°, A) → V
  85. Rotate(D', 240*°, A) → D''_1
  86. Segment(V, D''_1) → d''_1
  87. Rotate(D'_1, 240*°, A) → W
  88. Rotate(E', 240*°, A) → E''_1
  89. Segment(W, E''_1) → e''_1
  90. Rotate(E'_1, 240*°, A) → Z
  91. Rotate(F', 240*°, A) → F''_1
  92. Segment(Z, F''_1) → f''_1
  93. Rotate(F'_1, 240*°, A) → A_1
  94. Rotate(G', 240*°, A) → G''_2
  95. Segment(A_1, G''_2) → g''
  96. Rotate(G'_1, 240*°, A) → B_1
  97. Rotate(A'_1, 240*°, A) → C_1
  98. Segment(B_1, C_1) → h''
  99. Rotate(H, 240*°, A) → H'_2
  100. Rotate(J, 240*°, A) → J'_3
  101. Segment(H'_2, J'_3) → j'_3
  102. Rotate(J, 240*°, A) → J'_4
  103. Rotate(K, 240*°, A) → K'_3
  104. Segment(J'_4, K'_3) → k'_4
  105. Rotate(K, 240*°, A) → K'_4
  106. Rotate(C, 240*°, A) → C'_2
  107. Segment(K'_4, C'_2) → l'_1
  108. Rotate(H', 240*°, A) → H''
  109. Rotate(J', 240*°, A) → J''_1
  110. Segment(H'', J''_1) → j''_1
  111. Rotate(J'_1, 240*°, A) → D_1
  112. Rotate(K', 240*°, A) → K''_1
  113. Segment(D_1, K''_1) → k''_1
  114. Rotate(K'_1, 240*°, A) → E_1
  115. Rotate(C', 240*°, A) → C''
  116. Segment(E_1, C'') → l''
  117. Rotate(P, 240*°, A) → P'
  118. Rotate(Q, 240*°, A) → Q'
  119. Segment(P', Q') → m'
  120. Rotate(S, 240*°, A) → S'
  121. Rotate(R, 240*°, A) → R'
  122. Segment(S', R') → n'
  123. Rotate(T, 240*°, A) → T'
  124. Rotate(U, 240*°, A) → U'
  125. Segment(T', U') → q'
  126. Rotate(A', 240*°, A) → A''_1
  127. Rotate(B', 240*°, A) → B''
  128. Rotate(M, 240*°, A) → M'
  129. Rotate(A'', 240*°, A) → A'''
  130. Rotate(N, 240*°, A) → N'
  131. Rotate(O, 240*°, A) → O'
  132. Rotate(A'_2, 240*°, A) → F_1
  133. Rotate(G'_2, 240*°, A) → G_1
  134. Rotate(F'_2, 240*°, A) → H_1
  135. Rotate(E'_2, 240*°, A) → I_1
  136. Rotate(D'_2, 240*°, A) → J_1
  137. Rotate(B'_2, 240*°, A) → K_1
  138. Rotate(D'', 240*°, A) → D'''
  139. Rotate(E'', 240*°, A) → E'''
  140. Rotate(F'', 240*°, A) → F'''
  141. Rotate(G''_1, 240*°, A) → L_1
  142. Rotate(C'_1, 240*°, A) → M_1
  143. Rotate(K'_2, 240*°, A) → N_1
  144. Rotate(J'_2, 240*°, A) → O_1
  145. Rotate(H'_1, 240*°, A) → P_1
  146. Rotate(J'', 240*°, A) → J'''
  147. Rotate(K'', 240*°, A) → K'''
  148. Polygon(F_1, G_1, M_1, N_1, O_1, P_1, J''', K''', H_1, I_1, J_1, K_1, D''', E''', F''', L_1) → poly3'', f_3, l_1, m_1, n_1, o_1, p_1, j''', k''', g_3, h_3, i_1, j_3, k_3, d''', e''', f'''
  149. Rotate(p', 240*°, A) → p''
  150. Rotate(B'_3, 240*°, A) → Q_1
  151. Rotate(D'_3, 240*°, A) → R_1
  152. Segment(Q_1, R_1) → r
  153. Rotate(D'_4, 240*°, A) → S_1
  154. Rotate(E'_3, 240*°, A) → T_1
  155. Segment(S_1, T_1) → s
  156. Rotate(E'_4, 240*°, A) → U_1
  157. Rotate(F'_3, 240*°, A) → V_1
  158. Segment(U_1, V_1) → t
  159. Rotate(F'_4, 240*°, A) → W_1
  160. Rotate(G'_3, 240*°, A) → Z_1
  161. Segment(W_1, Z_1) → q_1
  162. Rotate(G'_4, 240*°, A) → A_2
  163. Rotate(A'_3, 240*°, A) → B_2
  164. Segment(A_2, B_2) → r_1
  165. Rotate(V, 240*°, A) → V'
  166. Rotate(D''_1, 240*°, A) → C_2
  167. Segment(V', C_2) → s_1
  168. Rotate(W, 240*°, A) → W'
  169. Rotate(E''_1, 240*°, A) → D_2
  170. Segment(W', D_2) → t_1
  171. Rotate(Z, 240*°, A) → Z'
  172. Rotate(F''_1, 240*°, A) → E_2
  173. Segment(Z', E_2) → i_2
  174. Rotate(A_1, 240*°, A) → F_2
  175. Rotate(G''_2, 240*°, A) → G_2
  176. Segment(F_2, G_2) → g'''
  177. Rotate(B_1, 240*°, A) → H_2
  178. Rotate(C_1, 240*°, A) → I_2
  179. Segment(H_2, I_2) → h'''
  180. Rotate(H'_2, 240*°, A) → J_2
  181. Rotate(J'_3, 240*°, A) → K_2
  182. Segment(J_2, K_2) → l_2
  183. Rotate(J'_4, 240*°, A) → L_2
  184. Rotate(K'_3, 240*°, A) → M_2
  185. Segment(L_2, M_2) → m_2
  186. Rotate(K'_4, 240*°, A) → N_2
  187. Rotate(C'_2, 240*°, A) → O_2
  188. Segment(N_2, O_2) → n_2
  189. Rotate(H'', 240*°, A) → H'''
  190. Rotate(J''_1, 240*°, A) → P_2
  191. Segment(H''', P_2) → p_2
  192. Rotate(D_1, 240*°, A) → Q_2
  193. Rotate(K''_1, 240*°, A) → R_2
  194. Segment(Q_2, R_2) → q_2
  195. Rotate(E_1, 240*°, A) → S_2
  196. Rotate(C'', 240*°, A) → C'''
  197. Segment(S_2, C''') → l'''
  198. Rotate(P', 240*°, A) → P''
  199. Rotate(Q', 240*°, A) → Q''
  200. Segment(P'', Q'') → m''
  201. Rotate(S', 240*°, A) → S''
  202. Rotate(R', 240*°, A) → R''
  203. Segment(S'', R'') → n''
  204. Rotate(T', 240*°, A) → T''
  205. Rotate(U', 240*°, A) → U''
  206. Segment(T'', U'') → q''
  207. Rotate(M, 240*°, A) → M'_1
  208. Rotate(C', 240*°, A) → C''_1
  209. Rotate(A'', 240*°, A) → A'''_1
  210. Rotate(A''_1, 240*°, A) → T_2
  211. Rotate(B'', 240*°, A) → B'''
  212. Rotate(M', 240*°, A) → M''
  213. Rotate(A''', 240*°, A) → U_2
  214. Rotate(N', 240*°, A) → N''
  215. Rotate(O', 240*°, A) → O''

AI Drawing Prompt Reference

Draw a triangle and rotate it around one vertex three times, each time by 120 degrees, to create six connected triangles forming a hexagon. Then, combine these triangles into a larger hexagon and draw a central symmetric pattern inside it, including diagonals and midpoints. Finally, add some decorative arcs and lines to enrich the design.
The prompt above was compiled from the original drawing commands and is for reference only.