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八面体的旋转对称性

八面体的旋转对称性
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2014-10-21 14:49
立体几何变换几何作图
本范例演示八面体的旋转对称性。核心数学概念包括旋转对称性和立体几何。通过使用GeoGebra命令如Octahedron、PointIn、Rotate等，构建了八面体的各个面和边。适合高中几何课程使用。

GeoGebra 命令及参数

  1. Octahedron(A, B, xOyPlane) → a, C, face6, face7, face8, edge1, edge2, edge3, edge4, edge5, edge6, edge7, D, edge8, edge9, edge10, edge11, edge12, E, F, face1, face2, face3, face4, face5
  2. PointIn(face8) → G
  3. PointIn(face1) → H
  4. Line(G, H) → b
  5. Rotate(face1, (-α), b) → face1'
  6. Rotate(face2, (-α), b) → face2'
  7. Rotate(face3, (-α), b) → face3'
  8. Rotate(face4, (-α), b) → face4'
  9. Rotate(face5, (-α), b) → face5'
  10. Rotate(face6, (-α), b) → face6'
  11. Rotate(face7, (-α), b) → face7'
  12. Rotate(face8, (-α), b) → face8'
  13. Circle(E, F, D) → e
  14. Circle(A, B, C) → f
  15. Center(e) → I
  16. Center(f) → J
  17. Midpoint(edge7) → K
  18. Midpoint(edge10) → L
  19. Midpoint(edge12) → M
  20. Midpoint(edge1) → N
  21. Midpoint(edge2) → O
  22. Midpoint(edge3) → P