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Rotational Symmetry of Tetrahedron by Anthony OR 柯志明

Rotational Symmetry of Tetrahedron by Anthony OR 柯志明
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2017-04-11 12:23
VectorSolid GeometryTransformationGeometric Construction
In collections Rotational Symmetries of Platonic Solids
This example demonstrates the rotational symmetry of a tetrahedron. Key math concepts include symmetry, circumcircle, 3D vectors, geometric mean, and angles. It is constructed using commands like Tetrahedron, Point, PointIn, Circle, Center, Line, Rotate, and Midpoint in GeoGebra, suitable for high school and above students studying solid geometry and symmetry.

GeoGebra Commands & Parameters

  1. Tetrahedron(A, B, xOyPlane) → a, C, edge4, edge5, edge6, D, face1, face2, face3, face4, edge1, edge2, edge3
  2. Point({edge4, edge5, edge6}) → E
  3. PointIn(face1) → F
  4. Circle(A, B, D) → e
  5. Circle(B, C, D) → f
  6. Circle(C, A, D) → g
  7. Circle(A, B, C) → h
  8. Center(h) → J
  9. Line(E, F) → b
  10. Rotate(face1, (-α), b) → face1'
  11. Rotate(face2, (-α), b) → face2'
  12. Rotate(face3, (-α), b) → face3'
  13. Rotate(face4, (-α), b) → face4'
  14. Midpoint(edge6) → K
  15. Midpoint(edge5) → L
  16. Midpoint(edge4) → M
  17. Midpoint(edge2) → N
  18. Midpoint(edge1) → O
  19. Midpoint(edge3) → P