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{5,3} Tessellation: Construction of a Regular Dodecahedron

{5,3} Tessellation: Construction of a Regular Dodecahedron
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2025-08-19 01:40
In collections Teselaciones regulares
This example demonstrates the 3D construction and dynamic visualization of a regular dodecahedron ({5,3} tessellation). Core mathematical concepts include regular polyhedra, tessellation theory, Euler's polyhedron formula, and pentagonal planar tessellation. Construction details: Using Sphere command for spherical positioning assistance, Sequence command to generate vertex sequences, CurveCartesia

GeoGebra Commands & Parameters

  1. Sphere(O, r) → a
  2. Sequence(Segment[Vdode2(k, 1), Vdode2(k, 2)], k, 1, 30) → segDode
  3. Sequence(CircleArc[(0, 0, 0), Vdode2(k, 1), Vdode2(k, 2)], k, 1, 30) → arcosDode
  4. Sphere(O, r) → a'
  5. CurveCartesian(If[t ≤ 1, V1 + (t * (V2 - V1)), 1 < t ≤ 2, V2 + ((t - 1) * (V3 - V2)), V3 + ((t - 2) * (V4 - V3))], t, 0, 3) → c5
  6. Surface((r; arg((k * c5(t)) + ((1 - k) * V5)); alt((k * c5(t)) + ((1 - k) * V5))), k, 0, 1, t, 0, 3) → s