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Rotational Symmetry of Octahedron

Rotational Symmetry of Octahedron
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2014-10-21 14:49
Solid GeometryTransformationGeometric Construction
This example demonstrates the rotational symmetry of an octahedron. Key mathematical concepts include rotational symmetry and solid geometry. Using GeoGebra commands such as Octahedron, PointIn, and Rotate, the faces and edges of the octahedron are constructed. Suitable for high school geometry courses.

GeoGebra Commands & Parameters

  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