MathPlotAI Logo MathPlotAI

Soccer Ball Construction

Soccer Ball Construction
Loading the math board and drawing, please wait…
2015-06-29 01:05
PolygonSolid GeometryTransformationGeometric Construction
This example demonstrates how to construct a soccer ball's geometric model by rotating polygons. Key math concepts include polygons, rotation, solid geometry, and spherical geometry. Construction highlights involve using GeoGebra commands like Polygon, Rotate, and Plane to rotate a regular pentagon, creating an approximation of a spherical surface. Suitable for high school solid geometry instruction and geometric construction practice, helping students understand the relationship between polyhedra and spheres.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 6) → poligon1, a, F, b, c, d, e, f, C, D, E
  2. Rotate(poligon1, 138*°, e) → poligon1'
  3. Rotate(E, -120*°, F, poligon1') → E'
  4. Rotate(F, -120*°, E', poligon1') → F'
  5. Rotate(E', -120*°, F', poligon1') → E''
  6. Rotate(F', -120*°, E'', poligon1') → F''
  7. Plane(E', F, A) → g
  8. Polygon(E', F, 5, g) → poligon2, h, i, j, k, l, G, H, I
  9. Plane(I, E', F') → m
  10. Polygon(I, E', 6, m) → poligon3, n, M, p, q, r, s, t, J, K, L
  11. Plane(H, I, M) → o
  12. Polygon(H, I, 6, o) → poligon4, a_1, Q, b_1, c_1, d_1, e_1, f_1, N, O, P
  13. Plane(Q, H, G) → u
  14. Polygon(Q, H, 6, u) → poligon5, g_1, U, h_1, i_1, j_1, k_1, l_1, R, S, T
  15. Plane(C, B, T) → v
  16. Polygon(B, T, 5, v) → poligon6, m_1, n_1, p_1, q_1, r_1, V, W, Z
  17. Plane(L, N, O) → w
  18. Polygon(L, N, 5, w) → poligon7, s_1, t_1, a_2, b_2, c_2, A_1, B_1, C_1
  19. Plane(F'', E, D) → o_1
  20. Polygon(F'', E, 5, o_1) → poligon8, d_2, e_2, f_2, g_2, h_2, D_1, E_1, F_1
  21. Plane(E_1, D, C) → u_1
  22. Polygon(E_1, D, 6, u_1) → poligon9, i_2, J_1, j_2, k_2, l_2, m_2, n_2, G_1, H_1, I_1
  23. Plane(F_1, E_1, J_1) → v_1
  24. Polygon(F_1, E_1, 6, v_1) → poligon10, p_2, N_1, q_2, r_2, s_2, t_2, a_3, K_1, L_1, M_1
  25. Plane(K, F', E'') → w_1
  26. Polygon(K, F', 5, w_1) → poligon11, b_3, c_3, d_3, e_3, f_3, O_1, P_1, Q_1
  27. Plane(P_1, O_1, F'') → o_2
  28. Polygon(P_1, O_1, 6, o_2) → poligon12, g_3, U_1, h_3, i_3, j_3, k_3, l_3, R_1, S_1, T_1
  29. Plane(I_1, H_1, V) → u_2
  30. Polygon(I_1, H_1, 6, u_2) → poligon13, m_3, A_2, n_3, p_3, q_3, r_3, s_3, V_1, W_1, Z_1
  31. Plane(L_1, J_1, I_1) → v_2
  32. Polygon(L_1, J_1, 5, v_2) → poligon14, t_3, a_4, b_4, c_4, d_4, B_2, C_2, D_2
  33. Plane(W_1, V, T) → w_2
  34. Polygon(W_1, V, 6, w_2) → poligon15, e_4, H_2, f_4, g_4, h_4, i_4, j_4, E_2, F_2, G_2
  35. Plane(G_2, U, Q) → o_3
  36. Polygon(G_2, U, 5, o_3) → poligon16, k_4, l_4, m_4, n_4, p_4, I_2, J_2, K_2
  37. Plane(Q_1, P_1, U_1) → u_3
  38. Polygon(Q_1, P_1, 6, u_3) → poligon17, q_4, O_2, r_4, s_4, t_4, a_5, b_5, L_2, M_2, N_2
  39. Plane(M_1, L_1, D_2) → v_3
  40. Polygon(M_1, L_1, 6, v_3) → poligon18, c_5, S_2, d_5, e_5, f_5, g_5, h_5, P_2, Q_2, R_2
  41. Plane(L_2, N_1, M_1) → w_3
  42. Plane(L_2, N_1, M_1) → o_4
  43. Polygon(L_2, N_1, 5, o_4) → poligon19, i_5, j_5, k_5, l_5, m_5, T_2, U_2, V_2
  44. Plane(Z_1, W_1, H_2) → u_4
  45. Polygon(Z_1, W_1, 5, u_4) → poligon20, n_5, p_5, q_5, r_5, s_5, W_2, Z_2, A_3
  46. Plane(W_2, G_2, K_2) → v_4
  47. Polygon(W_2, G_2, 6, v_4) → poligon21, t_5, E_3, a_6, b_6, c_6, d_6, e_6, B_3, C_3, D_3
  48. Plane(B_3, P, O) → w_4
  49. Plane(L, K, Q_1) → o_5
  50. Polygon(L, K, 6, o_5) → poligon22, f_6, I_3, g_6, h_6, i_6, j_6, k_6, F_3, G_3, H_3
  51. Plane(P_2, C_2, Z_1) → u_5
  52. Polygon(P_2, C_2, 6, u_5) → poligon23, l_6, M_3, m_6, n_6, p_6, q_6, r_6, J_3, K_3, L_3
  53. Plane(H_3, G_3, N_2) → v_5
  54. Polygon(H_3, G_3, 5, v_5) → poligon24, s_6, t_6, a_7, b_7, c_7, N_3, O_3, P_3
  55. Plane(H_3, C_1, B_1) → w_5
  56. Polygon(H_3, C_1, 6, w_5) → poligon25, d_7, T_3, e_7, f_7, g_7, h_7, i_7, Q_3, R_3, S_3
  57. Plane(U_2, V_2, N_2) → o_6
  58. Polygon(U_2, V_2, 6, o_6) → poligon26, j_7, Z_3, k_7, l_7, m_7, n_7, p_7, U_3, V_3, W_3
  59. Plane(L_3, M_3, R_2) → u_6
  60. Plane(L_3, M_3, W_3) → v_6
  61. Polygon(L_3, M_3, 5, v_6) → poligon27, q_7, r_7, s_7, t_7, a_8, A_4, B_4, C_4
  62. Plane(R_3, Q_3, A_1) → w_6
  63. Polygon(R_3, Q_3, 6, w_6) → poligon28, b_8, G_4, c_8, d_8, e_8, f_8, g_8, D_4, E_4, F_4
  64. Plane(P_3, S_3, C_4) → o_7
  65. Polygon(P_3, S_3, 6, o_7) → poligon29, h_8, K_4, i_8, j_8, k_8, l_8, m_8, H_4, I_4, J_4
  66. Plane(H_4, S_3, R_3) → u_7
  67. Polygon(H_4, S_3, 5, u_7) → poligon30, n_8, p_8, q_8, r_8, s_8, L_4, M_4, N_4
  68. Plane(E_3, A_3, L_3) → v_7
  69. Polygon(E_3, A_3, 6, v_7) → poligon31, t_8, R_4, a_9, b_9, c_9, d_9, e_9, O_4, P_4, Q_4