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5-fold Symmetry Pattern

5-fold Symmetry Pattern
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2019-12-31 22:29
PolygonTransformationGeometric Construction
This example demonstrates the 5-fold symmetry in Islamic geometric patterns. It involves geometric transformations such as mirroring and rotation, and the construction of polygons. Using GeoGebra commands like Intersect, Point, Polygon, Segment, Mirror, CircleArc, and PolyLine, a 5-fold symmetric geometric pattern can be constructed. Suitable for high school and above students to learn about geometric transformations and symmetry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 10) → veelhoek1, f, p, C, D, E, F, G, H, I, J, g, h, i, j, k, l, m, n
  4. Point(xAxis) → K
  5. Point(xAxis) → L
  6. Polygon(K, L, 10) → veelhoek2, q, f_1, M, N, O, P, Q, R, S, T, r, s, t, a, b, c, d, e
  7. Point(xAxis) → U
  8. Point(xAxis) → V
  9. Polygon(U, V, 10) → veelhoek3, g_1, q_1, W, Z, A_1, B_1, C_1, D_1, E_1, F_1, h_1, i_1, j_1, k_1, l_1, m_1, n_1, p_1
  10. Point(xAxis) → G_1
  11. Point(xAxis) → H_1
  12. Polygon(G_1, H_1, 10) → veelhoek4, r_1, g_2, I_1, J_1, K_1, L_1, M_1, N_1, O_1, P_1, s_1, t_1, a_1, b_1, c_1, d_1, e_1, f_2
  13. Segment(H, A) → h_2
  14. Segment(E, B) → i_2
  15. Segment(H, C) → j_2
  16. Segment(E, J) → k_2
  17. Polygon(A, B, 5) → veelhoek5, l_2, m_2, n_2, p_2, q_2, Q_1, R_1, S_1
  18. Segment(Q, L) → r_2
  19. Segment(P, K) → s_2
  20. Segment(R, O) → t_2
  21. Segment(T, M) → a_2
  22. Intersect(r_2, t_2) → T_1
  23. Intersect(r_2, s_2) → U_1
  24. Intersect(s_2, a_2) → V_1
  25. Polygon(R, S, T, V_1, U_1, T_1) → veelhoek6, r_3, s_3, t_3, v_1, u_1, b_2
  26. Segment(F_1, A_1) → c_4
  27. Segment(W, D_1) → d_4
  28. Segment(F_1, W) → c_2
  29. Mirror(U, c_2) → U'
  30. Mirror(V, c_2) → V'
  31. CircleArc(F_1, U, E_1) → e_4
  32. CircleArc(W, Z, V) → c_5
  33. Polygon(F_1, U, V, W, V', U') → veelhoek7, d_2, u, v, w, v', u'
  34. PolyLine(F_1, U', V', W) → e_2
  35. Segment(N_1, G_1) → f_3
  36. Segment(N_1, K_1) → g_3
  37. Segment(K_1, H_1) → h_3
  38. Mirror(O_1, f_3) → W_1
  39. Mirror(P_1, f_3) → Z_1
  40. Mirror(L_1, g_3) → A_2
  41. Mirror(I_1, h_3) → B_2
  42. Polygon(G_1, Z_1, W_1, N_1, O_1, P_1) → veelhoek8, i_3, z_1, w_1, j_3, o_1, k_3
  43. Polygon(N_1, W_1, A_2, K_1, L_1, M_1) → veelhoek9, l_3, m_3, n_3, p_3, q_3, a_3
  44. Polygon(K_1, A_2, B_2, H_1, I_1, J_1) → veelhoek10, b_3, c_3, d_3, e_3, f_4, g_4
  45. Polygon(W_1, Z_1, G_1, H_1, B_2, A_2) → veelhoek12, n_4, p_4, q_4, r_4, s_4, t_4
  46. Segment(N_1, W_1) → a_4
  47. Segment(A_2, K_1) → b_4
  48. Polygon(G_1, H_1, B_2, A_2, W_1, Z_1) → veelhoek11, h_4, i_4, j_4, k_4, l_4, m_4

AI Drawing Prompt Reference

Create a 5-fold symmetric pattern with five pentagons and connecting lines. Start by selecting five points on the x-axis and drawing five pentagons. Then use the vertices of these pentagons to draw connecting lines, forming the symmetric pattern.
The prompt above was compiled from the original drawing commands and is for reference only.