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Combination of Triangles and Pentagons: {3, 5} Icosahedron

Combination of Triangles and Pentagons: {3, 5} Icosahedron
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2025-08-19 01:39
In collections Teselaciones regulares
This example demonstrates how to use GeoGebra to create and explore the combination of triangles and pentagons, known as the {3, 5} icosahedron. This complex geometric shape involves core concepts in geometry and geometric construction. Using GeoGebra's Sphere, Sequence, CurveCartesian, Surface commands and objects such as b, r, O, a, Vico2, users can easily create and interact with this shape. Th

GeoGebra Commands & Parameters

  1. Sphere(O, r) → a
  2. Sequence(CircleArc[(0, 0, 0), Vico2(k, 1), Vico2(k, 2)], k, 1, 30) → arcosIco
  3. Sphere(O, r) → a'
  4. CurveCartesian(V1 + (t * (V2 - V1)), t, 0, 1) → c3
  5. Surface((r; arg((k * c3(t)) + ((1 - k) * V3)); alt((k * c3(t)) + ((1 - k) * V3))), k, 0, 1, t, 0, 1) → s