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Plane Tiling Example

Plane Tiling Example
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2020-07-15 21:50
PolygonGeometric Construction
This example demonstrates how to use GeoGebra tools for geometric constructions of plane tilings, involving concepts like polygonal tiling, symmetry, and spatial packing. It utilizes commands such as Tool3, Tool2, Tool1 and objects like A_7, B_4, poly1, f, g, h, i, C_7, D_4, poly2, j, k, l, m, E, F, poly3, n, p, q, r, K_3, poly6, L_3, g_1, h_1, i_1, j_1, M, poly7, N, k_1, l_1, m_1, n_1, O, P, p_1, q_1, r_1. Suitable for middle school students and above for learning geometric constructions and spatial geometry, or for classroom demonstrations.

GeoGebra Commands & Parameters

  1. Tool3(A_7) → B_4, poly1, f, g, h, i
  2. Tool3(C_7) → D_4, poly2, j, k, l, m
  3. Tool3(E) → F, poly3, n, p, q, r
  4. Tool2(K_3) → poly6, L_3, g_1, h_1, i_1, j_1
  5. Tool2(M) → poly7, N, k_1, l_1, m_1, n_1
  6. Tool1(O) → P, p_1, q_1, r_1, poly8
  7. Tool1(Q) → R, s_1, t_1, a_1, poly9
  8. Tool1(S) → T, b_1, c_1, d_1, poly10
  9. Tool1(U) → V, e_1, f_2, g_2, poly11
  10. Tool1(W) → Z, h_2, i_2, j_2, poly12
  11. Tool1(A_1) → B_1, k_2, l_2, m_2, poly13
  12. Tool1(C_1) → D_1, n_2, p_2, q_2, poly14
  13. Tool3(A_2) → B_2, poly1_1, f_3, g_3, h_3, i_3
  14. Tool3(C_2) → D_2, poly2_1, j_3, k_3, l_3, m_3
  15. Tool3(E_1) → F_1, poly3_1, n_3, p_3, q_3, r_2
  16. Tool2(G_1) → poly4_1, H_1, s_2, t_2, a_2, b_2
  17. Tool2(K_1) → poly6_1, L_1, g_4, h_4, i_4, j_4
  18. Tool2(M_1) → poly7_1, N_1, k_4, l_4, m_4, n_4
  19. Tool1(O_1) → P_1, p_4, q_4, r_3, poly8_1
  20. Tool1(Q_1) → R_1, s_3, t_3, a_3, poly9_1
  21. Tool1(S_1) → T_1, b_3, c_3, d_3, poly10_1
  22. Tool1(U_1) → V_1, e_3, f_5, g_5, poly11_1
  23. Tool1(W_1) → Z_1, h_5, i_5, j_5, poly12_1
  24. Tool1(A_3) → B_3, k_5, l_5, m_5, poly13_1
  25. Tool1(C_3) → D_3, n_5, p_5, q_5, poly14_1
  26. Tool2(G_2) → poly4_2, H_2, s_4, t_4, a_5, b_5
  27. Tool2(I_2) → poly5_2, J_2, c_4, d_4, e_4, f_6
  28. Tool2(K_2) → poly6_2, L_2, g_6, h_6, i_6, j_6

AI Drawing Prompt Reference

Draw a geometric plane tiling pattern showing complex structures formed by polygonal arrangements through symmetry and spatial packing. Start by constructing several base polygons, then use tools to combine them into larger units and repeat the arrangement to form a seamless tiling. Maintain geometric relationships and symmetry between parts, resulting in an aesthetically pleasing and mathematically beautiful plane pattern.
The prompt above was compiled from the original drawing commands and is for reference only.