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Symmetry in Sphere & Octahedron

Symmetry in Sphere & Octahedron
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2019-05-11 23:36
CirclePolygonSolid GeometryTransformationGeometric Construction
This example demonstrates the symmetry between a sphere and an octahedron in 3D space, highlighting geometric relationships. Key math concepts include symmetry, solid geometry, polygons, spheres, octahedrons, rotation, and intersection. GeoGebra commands used for construction are: Intersect, Circle, Sphere, Segment, Rotate, Polygon, Point, and Octahedron. It is suitable for high school students and math enthusiasts to explore spatial geometry and symmetry principles, ideal for classroom demonstrations or geometric investigations.

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. Octahedron(poly1, true) → e, A, faceAFG, edgeCG, edgeEG, edgeAC, edgeAG, edgeAD, edgeDF, edgeAF, edgeEF, edgeFG, F, G, faceCEG, faceACG, faceACD, faceADF, faceDEF, faceEFG
  16. Segment(A, planet) → p
  17. Segment(G, planet) → q
  18. Segment(F, planet) → r