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11 Patterns of the Cube (Net of a Cube)

11 Patterns of the Cube (Net of a Cube)
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2013-08-20 18:11
Solid GeometryGeometric Construction
This example demonstrates the 11 different nets of a cube, allowing users to observe through sliders and 3D viewpoint. Key math concepts include solid geometry, spatial visualization, and geometric transformations. It is constructed using commands like Vector, OrthogonalLine, Polygon, Midpoint, Translate, Segment, and Mirror in GeoGebra. Suitable for high school students or math enthusiasts exploring spatial geometry.

GeoGebra Commands & Parameters

  1. Vector(B_1, X) → u
  2. Vector(B_1, Z) → w
  3. OrthogonalLine(View3D, yAxis) → a_1
  4. OrthogonalLine(View3D, xAxis) → b_1
  5. Vector(B_1, Y) → v
  6. Polygon(L, K, N, M) → poly1, l, k_1, n, m
  7. Polygon(K, P, Q, N) → poly2, k_2, p, q, n_1
  8. Polygon(L, M, S, R) → poly3, l_1, m_1, s, r
  9. Polygon(N, V, W, M) → poly4, n_2, v_1, w_1, m_2
  10. Polygon(K, T, U, L) → poly5, k_3, t, u_1, l_2
  11. Polygon(B, Q, P, A) → poly6, b_2, q_1, p_1, a_2
  12. Midpoint(R, M) → D
  13. Translate(S, Vector[-(2.0 * v)]) → S'
  14. Segment(S, C) → e
  15. Translate(M, Vector[-(2.0) * v]) → M'
  16. Segment(M, E) → f
  17. Segment(E, C) → h
  18. Translate(N, Vector[-(2.0) * v]) → N'
  19. Translate(Q, Vector[-(2.0) * v]) → Q'_1
  20. Segment(Q, F) → i
  21. Segment(N, G) → j
  22. Segment(G, F) → d_1
  23. Translate(Q, Vector[-(2.0) * v]) → Q'_2
  24. Translate(B, Vector[-(2.0) * v]) → B'_1
  25. Segment(B, I) → e_1
  26. Segment(I, H) → f_1
  27. Segment(H, Q) → g_1
  28. Translate(K, Vector[2.0 * v]) → K'
  29. Translate(P, Vector[2.0 * v]) → P'_1
  30. Segment(P, J) → h_1
  31. Segment(J, A_1) → i_1
  32. Segment(A_1, K) → j_1
  33. Segment(B, H_1) → s_1
  34. Segment(H_1, C_1) → c
  35. Segment(C_1, A) → r_1
  36. Midpoint(N, P) → D_1
  37. Midpoint(k_1) → F_1
  38. Translate(A, Vector[2.0 * v]) → A'
  39. Translate(P, Vector[2.0 * v]) → P'
  40. Segment(A, G_1) → t_1
  41. Segment(G_1, I_1) → c_2
  42. Segment(I_1, P) → d_2
  43. Segment(J, K_1) → f_2
  44. Segment(P, L_1) → e_2
  45. Segment(L_1, K_1) → g_2
  46. Segment(M, W) → h_2
  47. Mirror(L_1, F_1) → O_1
  48. Mirror(K_1, F_1) → P_1
  49. Segment(M, M_1) → i_2
  50. Segment(N_1, J_1) → j_2
  51. Segment(J_1, M_1) → p_2
  52. Polygon(M, E, C, S) → poly7, q_2, r_2, s_2, t_2
  53. Polygon(Q, N, G, F) → poly8, q_3, n_3, g_3, f_3
  54. Polygon(B, Q, H, I) → poly9, b_3, q_4, h_3, i_3
  55. Polygon(J, A_1, K, P) → poly10, j_3, a_3, k_4, p_3
  56. Polygon(C_1, A, B, H_1) → poly11, c_3, a_4, b_4, h_4
  57. Polygon(G_1, I_1, P, A) → poly12, g_4, i_4, p_4, a_5
  58. Polygon(K_1, J, P, L_1) → poly13, k_5, j_4, p_5, l_3
  59. Polygon(M, M_1, J_1, N_1) → poly14, m_3, m_4, j_5, n_4

AI Drawing Prompt Reference

Draw 11 different nets of a cube, allowing observation through sliders and 3D viewpoints. Display multiple squares connected by edges to form faces, with some faces obtained via mirror and translation transformations, resulting in several distinct nets that illustrate spatial geometry and geometric transformations.
The prompt above was compiled from the original drawing commands and is for reference only.