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Step 5 Tessellation 2

Step 5 Tessellation 2
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2014-04-09 04:08
PolygonVectorGeometric Construction
In collections Hexagon- Translation Tessellation (Monster)
This example demonstrates the process of a five-step tessellation. It involves geometric transformations and polygons. Using commands like Polygon, Segment, Vector, and Translate, complex tessellation patterns can be constructed. Suitable for high school geometry and math enthusiasts.

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''

AI Drawing Prompt Reference

Draw a regular hexagon with vertices connected in order. From one side of the hexagon, construct a polyline path inward, connecting the two endpoints of that side to several interior points. Then, using a diagonal direction of the hexagon as a translation vector, translate the entire hexagon and its internal polyline once to create an adjacent copy. On another side of the hexagon, construct a second polyline path, and translate this part using another diagonal direction as the vector. The final result is a tessellation pattern with the original shape and its translated copies, all segments remaining parallel.
The prompt above was compiled from the original drawing commands and is for reference only.