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二十面体展开图

二十面体展开图
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2014-11-12 23:35
多边形立体几何
所属专题 3D Geometry & Cross Sections Surface Area and Volume Nets of 3D Figures 立体图形的折纸图样
这个范例展示了二十面体的展开图。二十面体是一种由20个等边三角形组成的正多面体。通过GeoGebra命令如Point、Icosahedron、Segment、Rotate等，可以构造出二十面体的展开图。适合初中及以上学生学习立体几何。

GeoGebra 命令及参数

  1. Point(Circle[Midpoint[A, B], (Distance[A, B] * sqrt(3) / 2), Segment[A, B]]) → C
  2. Icosahedron(A, B, C) → a, D, faceABC, faceACF, faceAFG, faceADG, faceABD, faceBDH, faceBEH, faceBCE, faceCEI, faceCFI, E, faceEHK, faceEIK, faceIKL, faceFIL, faceHJK, faceJKL, faceGJL, faceFGL, faceDHJ, faceDGJ, F, edgeAC, edgeAB, edgeBC, edgeAF, edgeCF, edgeAG, edgeFG, edgeAD, edgeDG, edgeBD, G, edgeBH, edgeDH, edgeBE, edgeEH, edgeCE, edgeCI, edgeEI, edgeFI, edgeEK, edgeHK, H, edgeIK, edgeIL, edgeKL, edgeFL, edgeJK, edgeHJ, edgeJL, edgeGL, edgeGJ, edgeDJ, I, J, K, L
  3. Segment(M, M + (0, 0, 2)) → b
  4. Point(b) → N
  5. Rotate(Polygon[A, B, D], (α * t), Segment[A, B]) → poly1
  6. Rotate(Polygon[A, D, G], (α * t), Segment[A, D]) → poly2
  7. Rotate(Polygon[B, D, H], (α * t), Segment[D, B]) → poly3
  8. Rotate(Polygon[G, D, J], (α * t), Segment[G, D]) → poly4
  9. Rotate(Polygon[D, H, J], (α * t), Segment[D, H]) → poly5
  10. Rotate(Polygon[G, J, L], (α * t), Segment[G, J]) → poly6
  11. Rotate(poly2, (α * t), Segment[A, B]) → poly2'
  12. Rotate(poly3, (α * t), Segment[A, B]) → poly3'
  13. Rotate(poly4, (α * t), Segment[A, D]) → poly4'
  14. Rotate(poly4', (α * t), Segment[A, B]) → poly4''
  15. Rotate(poly5, (α * t), Segment[D, B]) → poly5'
  16. Rotate(poly5', (α * t), Segment[A, B]) → poly5''
  17. Rotate(poly6, (α * t), Segment[G, D]) → poly6'
  18. Rotate(poly6', (α * t), Segment[A, D]) → poly6''
  19. Rotate(poly6'', (α * t), Segment[A, B]) → poly6'''
  20. Rotate(Polygon[J, K, L], (α * t), Segment[L, J]) → poly7
  21. Rotate(poly7, (α * t), Segment[G, J]) → poly7'
  22. Rotate(poly7', (α * t), Segment[G, D]) → poly7''
  23. Rotate(poly7'', (α * t), Segment[A, D]) → poly7'''
  24. Rotate(poly7''', (α * t), Segment[A, B]) → poly8
  25. Circle(A, B, C) → c
  26. Center(c) → O
  27. OrthogonalLine(O, Plane[A, B, C]) → d
  28. Rotate(poly1, 120°, d) → poly1'
  29. Rotate(poly2', 120°, d) → poly2''
  30. Rotate(poly3', 120°, d) → poly3''
  31. Rotate(poly4'', 120°, d) → poly4'''
  32. Rotate(poly5'', 120°, d) → poly5'''
  33. Rotate(poly6''', 120°, d) → poly9
  34. Rotate(poly1', 120°, d) → poly1''
  35. Rotate(poly2'', 120°, d) → poly2'''
  36. Rotate(poly3'', 120°, d) → poly3'''
  37. Rotate(poly4''', 120°, d) → poly10
  38. Rotate(poly5''', 120°, d) → poly11
  39. Rotate(poly9, 120°, d) → poly9'
  40. Polygon(A, B, C) → poly12, c_1, a_1, b_1
  41. Polygon(A, B, C) → poly13, c_2, a_2, b_2
  42. Rotate(poly1', 120°, d) → poly1''_1
  43. Rotate(Polygon[A, B, D], (α * t), Segment[A, B]) → poly14
  44. Rotate(poly1, 120°, d) → poly1'_1
  45. Rotate(poly3', 120°, d) → poly3''_1
  46. Rotate(poly2'', 120°, d) → poly2'''_1
  47. Rotate(poly2', 120°, d) → poly2''_1
  48. Rotate(poly2, (α * t), Segment[A, B]) → poly2'_1
  49. Rotate(poly3, (α * t), Segment[A, B]) → poly3'_1
  50. Rotate(poly5', (α * t), Segment[A, B]) → poly5''_1
  51. Rotate(poly4', (α * t), Segment[A, B]) → poly4''_1
  52. Rotate(poly6'', (α * t), Segment[A, B]) → poly6'''_1
  53. Rotate(poly7''', (α * t), Segment[A, B]) → poly15
  54. Rotate(poly3'', 120°, d) → poly3'''_1
  55. Rotate(poly5''', 120°, d) → poly16
  56. Rotate(poly4''', 120°, d) → poly17
  57. Rotate(poly9, 120°, d) → poly9'_1
  58. Rotate(poly5'', 120°, d) → poly5'''_1
  59. Rotate(poly4'', 120°, d) → poly4'''_1
  60. Rotate(poly6''', 120°, d) → poly18