Great triakis icosahedron

Polyhedron with 60 faces
Great triakis icosahedron
Type Star polyhedron
Face
Elements F = 60, E = 90
V = 32 (χ = 2)
Symmetry group Ih, [5,3], *532
Index references DU66
dual polyhedron Great stellated truncated dodecahedron
3D model of a great triakis icosahedron

In geometry, the great triakis icosahedron is a nonconvex isohedral polyhedron. It is the dual of the uniform great stellated truncated dodecahedron. Its faces are isosceles triangles. Part of each triangle lies within the solid, hence is invisible in solid models.

Proportions

The triangles have one angle of arccos ⁡ ( − 3 20 + 3 20 5 ) ≈ 79.314 951 312 25 ∘ {\displaystyle \arccos(-{\frac {3}{20}}+{\frac {3}{20}}{\sqrt {5}})\approx 79.314\,951\,312\,25^{\circ }} and two of arccos ⁡ ( 3 4 − 1 20 5 ) ≈ 50.342 524 343 87 ∘ {\displaystyle \arccos({\frac {3}{4}}-{\frac {1}{20}}{\sqrt {5}})\approx 50.342\,524\,343\,87^{\circ }} . The dihedral angle equals arccos ⁡ ( − 24 + 15 5 61 ) ≈ 81.001 410 024 84 ∘ {\displaystyle \arccos({\frac {-24+15{\sqrt {5}}}{61}})\approx 81.001\,410\,024\,84^{\circ }} .

See also

  • Triakis icosahedron

References

  • Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208

External links

  • Weisstein, Eric W. "Great triakis icosahedron". MathWorld.
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