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Dodecahedron Family

Dodecahedron Family
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2017-04-13 17:31
PolygonTrigonometrySolid GeometryTransformationGeometric Construction
This example demonstrates the construction and variations of a dodecahedron family. It involves core mathematical concepts such as polygons, rotations, reflections, sequences, and geometric transformations. Key GeoGebra commands used include Cube, Polygon, Sequence, Mirror, Rotate, and Union. Suitable for high school students and above, particularly for learning solid geometry and geometric transformations, as well as for math competitions or enrichment purposes.

GeoGebra Commands & Parameters

  1. Cube(B, A, a) → b, C, faceACGF, faceCDHG, faceEFGH, edgeBD, edgeAB, edgeAC, edgeCD, edgeBE, edgeDH, edgeEH, D, edgeEF, edgeAF, edgeFG, edgeCG, edgeGH, E, F, G, H, faceABDC, faceBDHE, faceABEF
  2. Polygon(S, E, N, P, F) → poly1, s, e, n, p, f
  3. Sequence(Rotate[poly1, ((n * 180))°, zAxis], n, 0, 1) → list1
  4. Mirror(list1, xOyPlane) → list1'
  5. Polygon(S, Q, G, L, F) → poly2, s_1, q, g, l, f_1
  6. Sequence(Rotate[poly2, ((n * 180))°, zAxis], n, 0, 1) → list2
  7. Mirror(list2, xOyPlane) → list2'
  8. Polygon(K, L, G, O, C) → poly3, k, l_1, g_1, o, c
  9. Sequence(Rotate[poly3, ((n * 180))°, zAxis], n, 0, 1) → list3
  10. Rotate(list3, 180°, xAxis) → list3'
  11. Union(list1, list1') → L1
  12. Union(list2, list2') → L2
  13. Union(list3, list3') → L3
  14. Union(L1, L2) → LL
  15. Union(LL, L3) → LLL