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Symmetry in Sphere & Icosahedron

Symmetry in Sphere & Icosahedron
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2019-05-11 21:51
Solid GeometryTransformationGeometric Construction
This example demonstrates the symmetry properties of a sphere and an icosahedron. It involves core mathematical concepts such as symmetry, spherical geometry, icosahedral structure, and geometric transformations. The construction utilizes GeoGebra commands and objects like Intersect, Circle, Sphere, Segment, Rotate, Polygon, Icosahedron, and Point. It is suitable for high school students and educators studying solid geometry, geometric transformations, and symmetry.

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. Icosahedron(poly1, true) → e, F, faceCEH, faceCHI, faceCFI, faceCDF, faceDFJ, faceDGJ, faceDEG, faceEGK, faceEHK, faceGJM, G, faceGKM, faceKMN, faceHKN, faceJLM, faceLMN, faceILN, faceHIN, faceFJL, faceFIL, edgeCH, H, edgeEH, edgeCI, edgeHI, edgeCF, edgeFI, edgeDF, edgeDJ, edgeFJ, edgeDG, edgeGJ, I, edgeEG, edgeEK, edgeGK, edgeHK, edgeGM, edgeJM, edgeKM, edgeKN, edgeMN, edgeHN, J, edgeLM, edgeJL, edgeLN, edgeIN, edgeIL, edgeFL, K, L, M, N
  12. Point(c) → planet
  13. Segment(B, planet) → l
  14. Segment(C, planet) → m
  15. Segment(D, planet) → n
  16. Segment(I, planet) → p
  17. Segment(F, planet) → q
  18. Segment(J, planet) → r
  19. Segment(L, planet) → s
  20. Segment(H, planet) → t
  21. Segment(N, planet) → f_1
  22. Segment(M, planet) → g_1
  23. Segment(G, planet) → h_1
  24. Segment(K, planet) → i_1