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三维立方体展开图

三维立方体展开图
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2020-04-29 19:40
多边形向量立体几何几何作图
①本范例演示了立方体的所有展开图及其在三维空间中的折叠效果；②涉及的核心数学概念包括立体几何、多边形构造、空间变换；③作图要点——运用了Sequence（序列）、Point（点）、Sum（求和）、If（条件判断）、Vector（向量）、Rotate（旋转）、Polygon（多边形）等GeoGebra命令与对象；④适合高中阶段学生及空间几何爱好者学习使用。

GeoGebra 命令及参数

  1. Sequence(D + (0, i), i, 0, 10) → LD
  2. Point(LD) → R
  3. Sum(Lc) → sumc
  4. If(n < 8, (-0.5, 0), (-1, -0.5)) → A_0
  5. Vector(A_0, (-0.5, -0.5)) → u
  6. Rotate(B + (2, 1), (t * π / 2), Line[B + (1, 1), B + (1, 0)]) → B1_2
  7. Rotate(B + (2, 2), (t * π / 2), Line[B + (1, 1), B + (1, 0)]) → B1_3
  8. Rotate(B + (1, 0), (t * π / 2), Line[F1_3, F1_4]) → F1_2
  9. Rotate(B, (t * π / 2), Line[F1_3, F1_4]) → F1_1
  10. Polygon(F1_1, F1_2, F1_3, F1_4) → qF1, s011, s012, s013, s014
  11. Rotate(B + (1, 3), (t * π / 2), Line[A1_4, A1_3]) → E1_3
  12. Rotate(B + (0, 3), (t * π / 2), Line[A1_4, A1_3]) → E1_4
  13. Polygon(E1_1, E1_2, E1_3, E1_4) → qE1, e09_1, e09_2, e09_3, e09_4
  14. Polygon(B1_1, B1_2, B1_3, B1_4) → qB1, e06_1, e06_2, e06_3, e06_4
  15. Rotate(C1_1 + Vector[B1_1, C1_1], (t * π / 2), Line[C1_4, C1_1]) → C1_2
  16. Rotate(C1_4 + Vector[B1_1, C1_1], (t * π / 2), Line[C1_4, C1_1]) → C1_3
  17. Polygon(C1_1, C1_2, C1_3, C1_4) → qC1, e07_1, e07_2, e07_3, e07_4
  18. Rotate(D1_1 + Vector[C1_1, D1_1], (t * π / 2), Line[D1_4, D1_1]) → D1_2
  19. Rotate(D1_4 + Vector[C1_1, D1_1], (t * π / 2), Line[D1_4, D1_1]) → D1_3
  20. Polygon(D1_1, D1_2, D1_3, D1_4) → qD1, e08_1, e08_2, e08_3, e08_4
  21. Polygon(A1_1, A1_2, A1_3, A1_4) → qA1, e05_1, e05_2, e05_3, e05_4
  22. Rotate(B1_3 + Vector[B1_2, B1_3], (t * π / 2), Line[B1_4, B1_3]) → E2_3
  23. Rotate(B1_4 + Vector[B1_1, B1_4], (t * π / 2), Line[B1_4, B1_3]) → E2_4
  24. Polygon(E2_1, E2_2, E2_3, E2_4) → qE2, e092_1, e092_2, e092_3, e092_4
  25. Rotate(C1_3 + Vector[C1_2, C1_3], (t * π / 2), Line[C1_4, C1_3]) → E3_3
  26. Rotate(C1_4 + Vector[C1_1, C1_4], (t * π / 2), Line[C1_4, C1_3]) → E3_4
  27. Polygon(E3_1, E3_2, E3_3, E3_4) → qE3, e093_1, e093_2, e093_3, e093_4
  28. Rotate(D1_3 + Vector[D1_2, D1_3], (t * π / 2), Line[D1_4, D1_3]) → E4_3
  29. Rotate(D1_4 + Vector[D1_1, D1_4], (t * π / 2), Line[D1_4, D1_3]) → E4_4
  30. Polygon(E4_1, E4_2, E4_3, E4_4) → qE4, e094_1, e094_2, e094_3, e094_4
  31. Rotate(B1_1 + Vector[B1_4, B1_1], (t * π / 2), Line[B1_2, B1_1]) → F2_1
  32. Rotate(B1_2 + Vector[B1_3, B1_2], (t * π / 2), Line[B1_2, B1_1]) → F2_2
  33. Polygon(F2_1, F2_2, F2_3, F2_4) → qF2, e012_1, e012_2, e012_3, e012_4
  34. If(n ≠ 7, (-2, -1.5), (-2.5, -1.5)) → B_1
  35. Polygon(A7_1, A7_2, A7_3, A7_4) → qA7, e067_1, e067_2, e067_3, e067_4
  36. Rotate(A7_2 + Vector[A7_1, A7_2], (t * π / 2), Line[(0.5, 0.5), (0.5, -0.5)]) → B7_2
  37. Rotate(A7_3 + Vector[A7_4, A7_3], (t * π / 2), Line[(0.5, 0.5), (0.5, -0.5)]) → B7_3
  38. Polygon(B7_1, B7_2, B7_3, B7_4) → qB7, f, g, h, i
  39. Rotate(B7_2 + Vector[B7_1, B7_2], (t * π / 2), Line[B7_3, B7_2]) → C7_2
  40. Rotate(B7_3 + Vector[B7_4, B7_3], (t * π / 2), Line[B7_3, B7_2]) → C7_3
  41. Polygon(C7_1, C7_2, C7_3, C7_4) → qC7, e077_1, e077_2, e077_3, e077_4
  42. Rotate(A7_1 + Vector[A7_4, A7_1], (t * π / 2), Line[A7_2, A7_1]) → F7_1
  43. Rotate(A7_2 + Vector[A7_4, A7_1], (t * π / 2), Line[A7_2, A7_1]) → F7_2
  44. Polygon(F7_1, F7_2, F7_3, F7_4) → qF7, f7_1, f7_2, f7_3, f7_4
  45. Rotate(F7_1 + Vector[F7_2, F7_1], (t * π / 2), Line[F7_1, F7_4]) → D7_1
  46. Rotate(F7_4 + Vector[F7_2, F7_1], (t * π / 2), Line[F7_1, F7_4]) → D7_4
  47. Polygon(D7_1, D7_2, D7_3, D7_4) → qD7, d7_1, d7_2, d7_3, d7_4
  48. Rotate(D7_4 + Vector[D7_2, D7_1], (t * π / 2), Line[D7_1, D7_4]) → E7_4
  49. Rotate(D7_1 + Vector[D7_2, D7_1], (t * π / 2), Line[D7_1, D7_4]) → E7_1
  50. Polygon(E7_1, E7_2, E7_3, E7_4) → qE7, e7_1, e7_2, e7_3, e7_4
  51. Rotate(A7_3 + Vector[A7_2, A7_3], (t * π / 2), Line[A7_4, A7_3]) → E8_3
  52. Rotate(A7_4 + Vector[A7_2, A7_3], (t * π / 2), Line[A7_4, A7_3]) → E8_4
  53. Polygon(E8_1, E8_2, E8_3, E8_4) → qE8, e8_1, e8_2, e8_3, e8_4
  54. Rotate(B7_3 + Vector[B7_2, B7_3], (t * π / 2), Line[B7_4, B7_3]) → E9_3
  55. Rotate(B7_4 + Vector[B7_2, B7_3], (t * π / 2), Line[B7_4, B7_3]) → E9_4
  56. Polygon(E9_1, E9_2, E9_3, E9_4) → qE9, e9_1, e9_2, e9_3, e9_4
  57. Rotate(C7_3 + Vector[C7_2, C7_3], (t * π / 2), Line[C7_4, C7_3]) → E10_3
  58. Rotate(C7_4 + Vector[C7_2, C7_3], (t * π / 2), Line[C7_4, C7_3]) → E10_4
  59. Polygon(E10_1, E10_2, E10_3, E10_4) → qE10, e10_1, e10_2, e10_3, e10_4
  60. Rotate(E9_2 + Vector[E9_4, E9_3], (t * π / 2), Line[E9_3, E9_2]) → C11_2
  61. Rotate(E9_3 + Vector[E9_4, E9_3], (t * π / 2), Line[E9_3, E9_2]) → C11_3
  62. Polygon(C11_1, C11_2, C11_3, C11_4) → qC11, c11_1, c11_2, c11_3, c11_4

AI 绘图提示语参考

展示一个立方体的所有可能展开图，这些展开图由多个正方形组成，可以折叠成一个立方体。首先绘制一个由多个正方形组成的平面图形，然后通过旋转和平移操作，生成多个类似的展开图，展示它们如何折叠成一个立方体。每个展开图都由四个正方形组成，它们通过共享边连接在一起。
以上提示语为根据原始绘图命令整理而来，仅供参考。