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Symmetry in Sphere & Tetrahedron

Symmetry in Sphere & Tetrahedron
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2019-05-11 22:47
Solid GeometryTransformationGeometric Construction
This example demonstrates the symmetry properties of spheres and tetrahedrons. It involves core mathematical concepts such as symmetry, spherical geometry, tetrahedral structures, and geometric transformations. The construction utilizes GeoGebra commands and objects like Intersect, Circle, Sphere, Segment, Rotate, Polygon, Point, and Tetrahedron. Suitable for high school students and geometry enthusiasts exploring solid geometry and symmetry principles.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → STAR
  2. Circle(STAR, a) → c
  3. Sphere(STAR, a) → b
  4. Circle(STAR, B, xOyPlane) → d
  5. Segment(STAR, B) → f
  6. Rotate(B, 120°, STAR) → C
  7. Segment(STAR, C) → g
  8. Rotate(C, 120°, STAR) → D
  9. Segment(STAR, D) → h
  10. Polygon(C, D, 3, xOyPlane) → poly1, i, j, k, E
  11. Point(c) → planet
  12. Segment(B, planet) → l
  13. Segment(C, planet) → m
  14. Segment(D, planet) → n
  15. Tetrahedron(poly1, true) → e, A, faceACE, faceACD, faceADE, edgeAC, edgeAE, edgeAD
  16. Segment(A, planet) → p