Possible Tessellations with Pentagrins

Possible Tessellations with Pentagrins
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2014-08-30 09:20
This example demonstrates the possibilities of tessellations with pentagons. It involves combinatorial geometry and uses commands like Pentagrin1, Pentagrin2 to construct various pentagon tessellations. Suitable for high school and above, this example is for exploring geometric transformations and tiling theory.

GeoGebra Commands & Parameters

  1. Pentagrin1(A, B) → poly1, a, b, c, d, e, C, D, E
  2. Pentagrin1(E, D) → poly2, f, g, h, i, j, F, G, H
  3. Pentagrin1(H, G) → poly3, k, l, m, n, p, I, J, K
  4. Pentagrin1(K, J) → poly4, q, r, s, t, a_1, L, M, N
  5. Pentagrin1(N, M) → poly5, b_1, c_1, d_1, e_1, f_1, O, P, Q
  6. Pentagrin1(Q, P) → poly6, g_1, h_1, i_1, j_1, k_1, R, S, T
  7. Pentagrin1(T, S) → poly7, l_1, m_1, n_1, p_1, q_1, U, V, W
  8. Pentagrin1(W, V) → poly8, r_1, s_1, t_1, a_2, b_2, Z, A_1, B_1
  9. Pentagrin1(B_1, A_1) → poly9, c_2, d_2, e_2, f_2, g_2, C_1, D_1, E_1
  10. Pentagrin1(E_1, D_1) → poly10, h_2, i_2, j_2, k_2, l_2, F_1, G_1, H_1
  11. Pentagrin2(G, D) → poly11, m_2, n_2, p_2, q_2, r_2, I_1, J_1, K_1
  12. Pentagrin2(G, K_1) → poly12, s_2, t_2, a_3, b_3, c_3, L_1, M_1, N_1
  13. Pentagrin2(G, N_1) → poly13, d_3, e_3, f_3, g_3, h_3, O_1, P_1, Q_1
  14. Pentagrin2(J, G) → poly14, i_3, j_3, k_3, l_3, m_3, R_1, S_1, T_1
  15. Pentagrin2(J, T_1) → poly15, n_3, p_3, q_3, r_3, s_3, U_1, V_1, W_1
  16. Pentagrin2(J, W_1) → poly16, t_3, a_4, b_4, c_4, d_4, Z_1, A_2, B_2
  17. Pentagrin2(M, J) → poly17, e_4, f_4, g_4, h_4, i_4, C_2, D_2, E_2
  18. Pentagrin2(M, E_2) → poly18, j_4, k_4, l_4, m_4, n_4, F_2, G_2, H_2
  19. Pentagrin2(M, H_2) → poly19, p_4, q_4, r_4, s_4, t_4, I_2, J_2, K_2
  20. Pentagrin2(P, M) → poly20, a_5, b_5, c_5, d_5, e_5, L_2, M_2, N_2
  21. Pentagrin2(P, N_2) → poly21, f_5, g_5, h_5, i_5, j_5, O_2, P_2, Q_2
  22. Pentagrin2(P, Q_2) → poly22, k_5, l_5, m_5, n_5, p_5, R_2, S_2, T_2
  23. Pentagrin2(S, P) → poly23, q_5, r_5, s_5, t_5, a_6, U_2, V_2, W_2
  24. Pentagrin2(S, W_2) → poly24, b_6, c_6, d_6, e_6, f_6, Z_2, A_3, B_3
  25. Pentagrin2(S, B_3) → poly25, g_6, h_6, i_6, j_6, k_6, C_3, D_3, E_3
  26. Pentagrin2(V, S) → poly26, l_6, m_6, n_6, p_6, q_6, F_3, G_3, H_3
  27. Pentagrin2(V, H_3) → poly27, r_6, s_6, t_6, a_7, b_7, I_3, J_3, K_3
  28. Pentagrin2(V, K_3) → poly28, c_7, d_7, e_7, f_7, g_7, L_3, M_3, N_3
  29. Pentagrin2(A_1, V) → poly29, h_7, i_7, j_7, k_7, l_7, O_3, P_3, Q_3
  30. Pentagrin2(A_1, Q_3) → poly30, m_7, n_7, p_7, q_7, r_7, R_3, S_3, T_3
  31. Pentagrin2(A_1, T_3) → poly31, s_7, t_7, a_8, b_8, c_8, U_3, V_3, W_3
  32. Pentagrin2(D_1, A_1) → poly32, d_8, e_8, f_8, g_8, h_8, Z_3, A_4, B_4
  33. Pentagrin2(D_1, B_4) → poly33, i_8, j_8, k_8, l_8, m_8, C_4, D_4, E_4
  34. Pentagrin2(D_1, E_4) → poly34, n_8, p_8, q_8, r_8, s_8, F_4, G_4, H_4
  35. Pentagrin2(B, D_1) → poly35, t_8, a_9, b_9, c_9, d_9, I_4, J_4, K_4
  36. Pentagrin2(B, K_4) → poly36, e_9, f_9, g_9, h_9, i_9, L_4, M_4, N_4
  37. Pentagrin2(B, N_4) → poly37, j_9, k_9, l_9, m_9, n_9, O_4, P_4, Q_4
  38. Pentagrin2(D, B) → poly38, p_9, q_9, r_9, s_9, t_9, R_4, S_4, T_4
  39. Pentagrin2(D, T_4) → poly39, a_{10}, b_{10}, c_{10}, d_{10}, e_{10}, U_4, V_4, W_4
  40. Pentagrin2(D, W_4) → poly40, f_{10}, g_{10}, h_{10}, i_{10}, j_{10}, Z_4, A_5, B_5
  41. Pentagrin2(Z_1, U_1) → poly41, k_{10}, l_{10}, m_{10}, n_{10}, p_{10}, C_5, D_5, E_5
  42. Pentagrin2(Z_1, E_5) → poly42, q_{10}, r_{10}, s_{10}, t_{10}, a_{11}, F_5, G_5, H_5
  43. Pentagrin2(F_2, Z_1) → poly43, b_{11}, c_{11}, d_{11}, e_{11}, f_{11}, I_5, J_5, K_5
  44. Pentagrin2(F_2, K_5) → poly44, g_{11}, h_{11}, i_{11}, j_{11}, k_{11}, L_5, M_5, N_5
  45. Pentagrin2(F_2, N_5) → poly45, l_{11}, m_{11}, n_{11}, p_{11}, q_{11}, O_5, P_5, Q_5
  46. Pentagrin2(I_2, F_2) → poly46, r_{11}, s_{11}, t_{11}, a_{12}, b_{12}, R_5, S_5, T_5
  47. Pentagrin2(I_2, T_5) → poly47, c_{12}, d_{12}, e_{12}, f_{12}, g_{12}, U_5, V_5, W_5
  48. Pentagrin2(O_2, I_2) → poly48, h_{12}, i_{12}, j_{12}, k_{12}, l_{12}, Z_5, A_6, B_6
  49. Pentagrin2(O_2, B_6) → poly49, m_{12}, n_{12}, p_{12}, q_{12}, r_{12}, C_6, D_6, E_6
  50. Pentagrin2(O_2, E_6) → poly50, s_{12}, t_{12}, a_{13}, b_{13}, c_{13}, F_6, G_6, H_6
  51. Pentagrin2(R_2, O_2) → poly51, d_{13}, e_{13}, f_{13}, g_{13}, h_{13}, I_6, J_6, K_6
  52. Pentagrin2(R_2, K_6) → poly52, i_{13}, j_{13}, k_{13}, l_{13}, m_{13}, L_6, M_6, N_6
  53. Pentagrin2(Z_2, R_2) → poly53, n_{13}, p_{13}, q_{13}, r_{13}, s_{13}, O_6, P_6, Q_6
  54. Pentagrin2(Z_2, Q_6) → poly54, t_{13}, a_{14}, b_{14}, c_{14}, d_{14}, R_6, S_6, T_6
  55. Pentagrin2(Z_2, T_6) → poly55, e_{14}, f_{14}, g_{14}, h_{14}, i_{14}, U_6, V_6, W_6
  56. Pentagrin2(C_3, Z_2) → poly56, j_{14}, k_{14}, l_{14}, m_{14}, n_{14}, Z_6, A_7, B_7
  57. Pentagrin2(C_3, B_7) → poly57, p_{14}, q_{14}, r_{14}, s_{14}, t_{14}, C_7, D_7, E_7
  58. Pentagrin2(I_3, C_3) → poly58, a_{15}, b_{15}, c_{15}, d_{15}, e_{15}, F_7, G_7, H_7
  59. Pentagrin2(I_3, H_7) → poly59, f_{15}, g_{15}, h_{15}, i_{15}, j_{15}, I_7, J_7, K_7
  60. Pentagrin2(I_3, K_7) → poly60, k_{15}, l_{15}, m_{15}, n_{15}, p_{15}, L_7, M_7, N_7
  61. Pentagrin2(L_3, I_3) → poly61, q_{15}, r_{15}, s_{15}, t_{15}, a_{16}, O_7, P_7, Q_7
  62. Pentagrin2(L_3, Q_7) → poly62, b_{16}, c_{16}, d_{16}, e_{16}, f_{16}, R_7, S_7, T_7
  63. Pentagrin2(R_3, L_3) → poly63, g_{16}, h_{16}, i_{16}, j_{16}, k_{16}, U_7, V_7, W_7
  64. Pentagrin2(R_3, W_7) → poly64, l_{16}, m_{16}, n_{16}, p_{16}, q_{16}, Z_7, A_8, B_8
  65. Pentagrin2(R_3, B_8) → poly65, r_{16}, s_{16}, t_{16}, a_{17}, b_{17}, C_8, D_8, E_8
  66. Pentagrin2(U_3, R_3) → poly66, c_{17}, d_{17}, e_{17}, f_{17}, g_{17}, F_8, G_8, H_8
  67. Pentagrin2(U_3, H_8) → poly67, h_{17}, i_{17}, j_{17}, k_{17}, l_{17}, I_8, J_8, K_8
  68. Pentagrin2(C_4, U_3) → poly68, m_{17}, n_{17}, p_{17}, q_{17}, r_{17}, L_8, M_8, N_8
  69. Pentagrin2(C_4, N_8) → poly69, s_{17}, t_{17}, a_{18}, b_{18}, c_{18}, O_8, P_8, Q_8
  70. Pentagrin2(C_4, Q_8) → poly70, d_{18}, e_{18}, f_{18}, g_{18}, h_{18}, R_8, S_8, T_8
  71. Pentagrin2(F_4, C_4) → poly71, i_{18}, j_{18}, k_{18}, l_{18}, m_{18}, U_8, V_8, W_8
  72. Pentagrin2(F_4, W_8) → poly72, n_{18}, p_{18}, q_{18}, r_{18}, s_{18}, Z_8, A_9, B_9
  73. Pentagrin2(L_4, F_4) → poly73, t_{18}, a_{19}, b_{19}, c_{19}, d_{19}, C_9, D_9, E_9
  74. Pentagrin2(L_4, E_9) → poly74, e_{19}, f_{19}, g_{19}, h_{19}, i_{19}, F_9, G_9, H_9
  75. Pentagrin2(L_4, H_9) → poly75, j_{19}, k_{19}, l_{19}, m_{19}, n_{19}, I_9, J_9, K_9
  76. Pentagrin2(O_4, L_4) → poly76, p_{19}, q_{19}, r_{19}, s_{19}, t_{19}, L_9, M_9, N_9
  77. Pentagrin2(O_4, N_9) → poly77, a_{20}, b_{20}, c_{20}, d_{20}, e_{20}, O_9, P_9, Q_9
  78. Pentagrin2(U_4, O_4) → poly78, f_{20}, g_{20}, h_{20}, i_{20}, j_{20}, R_9, S_9, T_9
  79. Pentagrin2(U_4, T_9) → poly79, k_{20}, l_{20}, m_{20}, n_{20}, p_{20}, U_9, V_9, W_9
  80. Pentagrin2(U_4, W_9) → poly80, q_{20}, r_{20}, s_{20}, t_{20}, a_{21}, Z_9, A_{10}, B_{10}
  81. Pentagrin2(I_1, U_4) → poly81, b_{21}, c_{21}, d_{21}, e_{21}, f_{21}, C_{10}, D_{10}, E_{10}
  82. Pentagrin2(I_1, E_{10}) → poly82, g_{21}, h_{21}, i_{21}, j_{21}, k_{21}, F_{10}, G_{10}, H_{10}
  83. Pentagrin2(L_1, I_1) → poly83, l_{21}, m_{21}, n_{21}, p_{21}, q_{21}, I_{10}, J_{10}, K_{10}
  84. Pentagrin2(L_1, K_{10}) → poly84, r_{21}, s_{21}, t_{21}, a_{22}, b_{22}, L_{10}, M_{10}, N_{10}
  85. Pentagrin2(L_1, N_{10}) → poly85, c_{22}, d_{22}, e_{22}, f_{22}, g_{22}, O_{10}, P_{10}, Q_{10}
  86. Pentagrin2(O_1, L_1) → poly86, h_{22}, i_{22}, j_{22}, k_{22}, l_{22}, R_{10}, S_{10}, T_{10}
  87. Pentagrin2(O_1, T_{10}) → poly87, m_{22}, n_{22}, p_{22}, q_{22}, r_{22}, U_{10}, V_{10}, W_{10}
  88. Pentagrin2(U_1, O_1) → poly88, s_{22}, t_{22}, a_{23}, b_{23}, c_{23}, Z_{10}, A_{11}, B_{11}
  89. Pentagrin2(U_1, B_{11}) → poly89, d_{23}, e_{23}, f_{23}, g_{23}, h_{23}, C_{11}, D_{11}, E_{11}
  90. Pentagrin2(U_1, E_{11}) → poly90, i_{23}, j_{23}, k_{23}, l_{23}, m_{23}, F_{11}, G_{11}, H_{11}

AI Drawing Prompt Reference

Create a tiling pattern made of multiple pentagons using the Pentagrin1 and Pentagrin2 commands, starting from point A and B, and sequentially constructing multiple pentagons where each pentagon's vertices connect to the vertices of the previous pentagon, forming a complex tiling pattern.
The prompt above was compiled from the original drawing commands and is for reference only.