Regular Hexagonal Tessellation

Regular Hexagonal Tessellation
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2022-05-05 13:57
This example demonstrates the construction of a regular hexagonal tessellation. It involves key mathematical concepts such as equilateral triangles and straight lines. Using GeoGebra commands like Intersect, Point, Polygon, Vector, and Translate, a regular hexagonal tessellation can be constructed. Suitable for middle school and above students to learn geometric construction.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 3) → poly1, f, g, h, C
  4. Polygon(C, B, 3) → poly2, i, j, k, D
  5. Polygon(C, D, 3) → poly3, l, m, n, E
  6. Polygon(C, E, 3) → poly4, p, q, r, F
  7. Polygon(C, F, 3) → poly5, s, t, a, G
  8. Polygon(C, G, 3) → poly6, b, c, d, H
  9. Polygon(D, B, 3) → poly7, e, f_1, g_1, I
  10. Polygon(D, I, 3) → poly8, h_1, i_1, j_1, J
  11. Polygon(D, J, 3) → poly9, k_1, l_1, m_1, K
  12. Polygon(D, K, 3) → poly10, n_1, p_1, q_1, L
  13. Polygon(J, I, 3) → poly11, r_1, s_1, t_1, M
  14. Polygon(J, M, 3) → poly12, a_1, b_1, c_1, N
  15. Polygon(J, N, 3) → poly13, d_1, e_1, f_2, O
  16. Polygon(J, O, 3) → poly14, g_2, h_2, i_2, P
  17. Polygon(N, M, 3) → poly15, j_2, k_2, l_2, Q
  18. Polygon(N, Q, 3) → poly16, m_2, n_2, p_2, R
  19. Polygon(N, R, 3) → poly17, q_2, r_2, s_2, S
  20. Polygon(N, S, 3) → poly18, t_2, a_2, b_2, T
  21. Polygon(B, A, 3) → poly19, c_2, d_2, e_2, U
  22. Polygon(I, B, 3) → poly20, f_3, g_3, h_3, V
  23. Polygon(M, I, 3) → poly21, i_3, j_3, k_3, W
  24. Polygon(Q, M, 3) → poly22, l_3, m_3, n_3, Z
  25. Polygon(W, Z, 3) → poly23, p_3, q_3, r_3, A_1
  26. Polygon(V, W, 3) → poly24, s_3, t_3, a_3, B_1
  27. Polygon(U, V, 3) → poly25, b_3, c_3, d_3, C_1
  28. Polygon(U, A, 3) → poly26, e_3, f_4, g_4, D_1
  29. Polygon(A, G, 3) → poly27, h_4, i_4, j_4, E_1
  30. Polygon(E_1, D_1, 3) → poly28, k_4, l_4, m_4, F_1
  31. Vector(A, U) → u
  32. Translate(poly19, u) → poly19'
  33. Translate(poly20, u) → poly20'
  34. Translate(poly23, u) → poly23'
  35. Translate(poly21, u) → poly21'
  36. Translate(poly24, u) → poly24'
  37. Translate(poly25, u) → poly25'
  38. Translate(poly28, u) → poly28'
  39. Translate(poly26, u) → poly26'
  40. Translate(poly22, u) → poly22'
  41. Translate(poly15, u) → poly15'
  42. Translate(poly16, u) → poly16'
  43. Translate(poly17, u) → poly17'
  44. Translate(poly15', u) → poly15''
  45. Translate(poly17', u) → poly17''
  46. Translate(poly16', u) → poly16''
  47. Translate(poly28', u) → poly28''
  48. Translate(poly26', u) → poly26''
  49. Translate(poly19', u) → poly19''
  50. Translate(poly25', u) → poly25''
  51. Translate(poly20', u) → poly20''
  52. Translate(poly24', u) → poly24''
  53. Translate(poly23', u) → poly23''
  54. Translate(poly21', u) → poly21''
  55. Translate(poly15'', u) → poly15'''
  56. Translate(poly22', u) → poly22''
  57. Polygon(S, R, 3) → poly29, n_4, p_4, q_4, G_1
  58. Polygon(G_1, R, 3) → poly30, r_4, s_4, t_4, H_1
  59. Polygon(H_1, R, 3) → poly31, a_4, b_4, c_4, I_1
  60. Polygon(G_1, H_1, 3) → poly32, d_4, e_4, f_5, J_1
  61. Polygon(J_1, H_1, 3) → poly33, g_5, h_5, i_5, K_1
  62. Polygon(J_1, K_1, 3) → poly34, j_5, k_5, l_5, L_1
  63. Translate(poly30, u) → poly30'
  64. Translate(poly32, u) → poly32'
  65. Translate(poly33, u) → poly33'
  66. Translate(poly34, u) → poly34'
  67. Translate(poly31, u) → poly31'
  68. Translate(poly30', u) → poly30''
  69. Translate(poly32', u) → poly32''
  70. Translate(poly17'', u) → poly17'''
  71. Translate(poly31', u) → poly31''
  72. Translate(poly30'', u) → poly30'''
  73. Translate(poly16'', u) → poly16'''
  74. Translate(poly17''', u) → t1
  75. Translate(poly31'', u) → poly31'''
  76. Polygon(D_1, E_1, 3) → poly35, m_5, n_5, p_5, M_1
  77. Polygon(D_1, M_1, 3) → poly36, q_5, r_5, s_5, N_1
  78. Polygon(D_1, N_1, 3) → poly37, t_5, a_5, b_5, O_1
  79. Polygon(O_1, N_1, 3) → poly38, c_5, d_5, e_5, P_1
  80. Polygon(O_1, P_1, 3) → poly39, f_6, g_6, h_6, Q_1
  81. Polygon(G, F, 3) → poly40, i_6, j_6, k_6, R_1
  82. Polygon(G, R_1, 3) → poly41, l_6, m_6, n_6, S_1
  83. Polygon(G, S_1, 3) → poly42, p_6, q_6, r_6, T_1
  84. Polygon(P_1, N_1, 3) → poly44, b_6, c_6, d_6, V_1

AI Drawing Prompt Reference

Draw a regular hexagonal tessellation starting from the origin, with the first equilateral triangle formed by the intersection of the x-axis and y-axis. Expand outward by connecting adjacent triangles at shared vertices, creating a continuous grid of equilateral triangles and regular hexagons, resulting in a seamless pattern of interconnected shapes.
The prompt above was compiled from the original drawing commands and is for reference only.