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Cube Nets by Kevin Westrich

Cube Nets by Kevin Westrich
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2016-05-05 19:45
PolygonSolid GeometryGeometric Construction
This example demonstrates the nets of a cube and their folding into 3D shapes. Core math concepts include solid geometry, polygon assembly, and spatial visualization. Construction involves commands like Vector, Translate, OrthogonalLine, Polygon, Midpoint, Segment, and Mirror. Suitable for middle school students and above learning 3D geometry and spatial reasoning.

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 six square faces. Start by drawing six squares, then connect them using translations and reflections to form the net. Ensure that the edges of each square align with the adjacent squares.
The prompt above was compiled from the original drawing commands and is for reference only.