MathPlotAI Logo MathPlotAI

Eleven Patterns of the Cube by Nolan

Eleven Patterns of the Cube by Nolan
Loading the math board and drawing, please wait…
2015-08-07 19:33
Solid GeometryTransformationGeometric Construction
This example demonstrates the eleven possible patterns of a cube's net. It involves the concepts of solid geometry, specifically the unfolding and folding of a cube. Using commands like Vector, Translate, and Mirror, various net patterns of the cube can be constructed. Suitable for middle school and above students to learn solid geometry and spatial visualization.

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 the eleven possible nets of a cube by first defining three orthogonal vectors, then translating a base square along these vectors to create adjacent squares, using orthogonal lines to set the drawing plane, constructing six square faces, marking the midpoints of edges, translating vertices back along the vectors to form corresponding points, connecting segments to outline each net, and finally mirroring points across midpoints to complete the remaining two net patterns.
The prompt above was compiled from the original drawing commands and is for reference only.