Great truncated icosidodecahedron

Great truncated icosidodecahedron
Type Uniform star polyhedron
Elements F = 62, E = 180
V = 120 (χ = 2)
Faces by sides 30{4}+20{6}+12{10/3}
Coxeter diagram
Wythoff symbol 2 3 5/3 |
Symmetry group Ih, [5,3], *532
Index references U68, C87, W108
Dual polyhedron Great disdyakis triacontahedron
Vertex figure
4.6.10/3
Bowers acronym Gaquatid

In geometry, the great truncated icosidodecahedron (or great quasitruncated icosidodecahedron or stellatruncated icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U68. It has 62 faces (30 squares, 20 hexagons, and 12 decagrams), 180 edges, and 120 vertices.[1] It is given a Schläfli symbol t0,1,2{5/3,3}, and Coxeter-Dynkin diagram, .

3D model of a great truncated icosidodecahedron

Cartesian coordinates

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Cartesian coordinates for the vertices of a great truncated icosidodecahedron centered at the origin are all the even permutations of  

where   is the golden ratio.

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Great disdyakis triacontahedron

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Great disdyakis triacontahedron
 
Type Star polyhedron
Face  
Elements F = 120, E = 180
V = 62 (χ = 2)
Symmetry group Ih, [5,3], *532
Index references DU68
dual polyhedron Great truncated icosidodecahedron
 
3D model of a great disdyakis triacontahedron

The great disdyakis triacontahedron (or trisdyakis icosahedron) is a nonconvex isohedral polyhedron. It is the dual of the great truncated icosidodecahedron. Its faces are triangles.


Proportions

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The triangles have one angle of  , one of   and one of   The dihedral angle equals   Part of each triangle lies within the solid, hence is invisible in solid models.

See also

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References

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  1. ^ Maeder, Roman. "68: great truncated icosidodecahedron". MathConsult.
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