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二十面体的旋转对称性

二十面体的旋转对称性
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2014-10-21 15:34
立体几何变换几何作图
所属专题 Rotational Symmetries of Platonic Solids
①本范例演示二十面体的旋转对称性；②涉及核心数学概念包括旋转、立体几何、对称、几何变换；③作图要点使用了 GeoGebra 命令：Icosahedron（二十面体）、Circle（圆）、Center（中心）、Midpoint（中点）、PointIn（点在...内）、Line（线）、Rotate（旋转）；④适合高中及以上学生及数学爱好者学习立体几何与对称变换。

GeoGebra 命令及参数

  1. Icosahedron(A, B, xOyPlane) → a, C, L, face1, face2, face3, face4, face5, face6, face7, face8, face9, D, face10, face11, face12, face13, face14, face15, face16, face17, face18, face19, E, face20, edge1, edge2, edge3, edge4, edge5, edge6, edge7, edge8, edge9, F, edge10, edge11, edge12, edge13, edge14, edge15, edge16, edge17, edge18, edge19, G, edge20, edge21, edge22, edge23, edge24, edge25, edge26, edge27, edge28, edge29, H, edge30, I, J, K
  2. Circle(J, K, L) → e
  3. Circle(A, B, C) → f
  4. Center(e) → M
  5. Center(f) → N
  6. Midpoint(edge27) → O
  7. Midpoint(edge25) → P
  8. Midpoint(edge23) → Q
  9. Midpoint(edge1) → R
  10. Midpoint(edge2) → S
  11. Midpoint(edge3) → T
  12. PointIn(face16) → U
  13. PointIn(face1) → V
  14. Line(U, V) → b
  15. Rotate(face1, (-α), b) → face1'
  16. Rotate(face10, (-α), b) → face10'
  17. Rotate(face11, (-α), b) → face11'
  18. Rotate(face12, (-α), b) → face12'
  19. Rotate(face13, (-α), b) → face13'
  20. Rotate(face14, (-α), b) → face14'
  21. Rotate(face15, (-α), b) → face15'
  22. Rotate(face16, (-α), b) → face16'
  23. Rotate(face17, (-α), b) → face17'
  24. Rotate(face18, (-α), b) → face18'
  25. Rotate(face19, (-α), b) → face19'
  26. Rotate(face2, (-α), b) → face2'
  27. Rotate(face20, (-α), b) → face20'
  28. Rotate(face3, (-α), b) → face3'
  29. Rotate(face4, (-α), b) → face4'
  30. Rotate(face5, (-α), b) → face5'
  31. Rotate(face6, (-α), b) → face6'
  32. Rotate(face7, (-α), b) → face7'
  33. Rotate(face8, (-α), b) → face8'
  34. Rotate(face9, (-α), b) → face9'

AI 绘图提示语参考

画一个二十面体，并展示其旋转对称性。首先绘制二十面体的各个面和边，然后以其中一条边为旋转轴，将一个面按一定角度旋转，接着依次将其他面也进行相同的旋转，最终呈现出二十面体旋转后的对称形态。
以上提示语为根据原始绘图命令整理而来，仅供参考。