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Cube Nets by azb

Cube Nets by azb
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2014-12-04 23:04
VectorSolid GeometryGeometric Construction
This example demonstrates the 11 nets of a cube. Using commands like Vector, Translate, and Mirror, it provides a clear visualization of the cube's geometric construction. Suitable for middle school and above students learning solid geometry.

GeoGebra Commands & Parameters

  1. Vector(B_1, Z) → w
  2. Vector(B_1, Y) → v
  3. Vector(B_1, X) → u
  4. Translate(A, Vector[(2 * v)]) → A'
  5. Translate(P, Vector[(2 * v)]) → P'
  6. OrthogonalLine(View3D, yAxis) → a_1
  7. OrthogonalLine(View3D, xAxis) → b_1
  8. Polygon(L, K, N, M) → poly1, l, k_1, n, m
  9. Polygon(K, P, Q, N) → poly2, k_2, p, q, n_1
  10. Polygon(L, M, S, R) → poly3, l_1, m_1, s, r
  11. Polygon(N, V, W, M) → poly4, n_2, v_1, w_1, m_2
  12. Polygon(K, T, U, L) → poly5, k_3, t, u_1, l_2
  13. Polygon(B, Q, P, A) → poly6, b_2, q_1, p_1, a_2
  14. Midpoint(R, M) → D
  15. Translate(S, Vector[(-((2 * v)))]) → S'
  16. Segment(S, C) → e
  17. Translate(M, Vector[((-2) * v)]) → M'
  18. Segment(M, E) → f
  19. Segment(E, C) → h
  20. Translate(N, Vector[((-2) * v)]) → N'
  21. Translate(Q, Vector[((-2) * v)]) → Q'_1
  22. Segment(Q, F) → i
  23. Segment(N, G) → j
  24. Segment(G, F) → d_1
  25. Translate(Q, Vector[((-2) * v)]) → Q'_2
  26. Translate(B, Vector[((-2) * v)]) → B'_1
  27. Segment(B, I) → e_1
  28. Segment(I, H) → f_1
  29. Segment(H, Q) → g_1
  30. Translate(K, Vector[(2 * v)]) → K'
  31. Translate(P, Vector[(2 * v)]) → P'_1
  32. Segment(P, J) → h_1
  33. Segment(J, A_1) → i_1
  34. Segment(A_1, K) → j_1
  35. Segment(B, H_1) → s_1
  36. Segment(H_1, C_1) → c
  37. Segment(C_1, A) → r_1
  38. Midpoint(N, P) → D_1
  39. Midpoint(k_1) → F_1
  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 a cube net with 11 faces. Start by drawing the three edge vectors u, v, and w. Then use translation and mirroring to create the other faces. First draw the initial three faces, then sequentially draw the remaining faces, ensuring each face is correctly connected to its adjacent faces.
The prompt above was compiled from the original drawing commands and is for reference only.