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Cube Nets (11 Patterns)

Cube Nets (11 Patterns)
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2020-11-02 01:13
PolygonSolid GeometryTransformationGeometric ConstructionSlider Animation
① This example demonstrates all 11 distinct nets of a cube, showing the correspondence between the 3D solid and its 2D unfolded patterns through an interactive 3D view. ② Core mathematical concepts include solid geometry, surface nets of a cube, spatial visualization, transformations between plane and solid, and symmetry. ③ Construction highlights: The GeoGebra commands used include Vector, Translate, OrthogonalLine, Polygon, Midpoint, Segment, and Mirror, along with 3D view objects (View3D), rotation parameters (sinphi, cosphi, sintheta, costheta), and multiple auxiliary points (A, P, O, etc.) and faces (poly1). The different net layouts are generated via translations and reflections. ④ Suitable for middle school to high school students learning solid geometry and developing spatial reasoning, as well as for teachers creating interactive lessons or students exploring all possible cube net configurations.

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

In a 3D coordinate view, set up mutually orthogonal axes to define the unfolding directions. Construct an initial quadrilateral face as a polygon (four corner points). Create adjacent square faces by translating the corresponding points by fixed multiples of the same direction vectors, producing several connected polygons that form a cube net. Then obtain the remaining symmetric faces using reflections across the appropriate lines determined by edge midpoints. Continue translating the newly created points to place all faces consistently in one plane. Finally, draw segment edges to show the shared boundaries between faces and add midpoints to indicate the key symmetry/hinge locations.
The prompt above was compiled from the original drawing commands and is for reference only.