Great truncated icosidodecahedron

Great truncated icosidodecahedron
TypeUniform star polyhedron
ElementsF = 62, E = 180
V = 120 (χ = 2)
Faces by sides30{4}+20{6}+12{10/3}
Wythoff symbol2 3 5/3 |
Symmetry groupIh, [5,3], *532
Index referencesU68, C87, W108
Dual polyhedronGreat disdyakis triacontahedron
Vertex figure
4.6.10/3
Bowers acronymGaquatid

In geometry, the great truncated icosidodecahedron or great quasitruncated icosidodecahedron is a nonconvex uniform polyhedron, indexed as U68. It is given a Schläfli symbol t0,1,2{5/3,3}, and Coxeter-Dynkin diagram, .

Cartesian coordinates

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

(±τ, ±τ, ±(3−1/τ)),
(±2τ, ±1/τ, ±(1−2/τ)),
(±τ, ±1/τ2, ±(1+3/τ)),
(±(1+2/τ), ±2, ±(2−1/τ)) and
(±1/τ, ±3, ±2/τ),

where τ = (1+√5)/2 is the golden ratio.

Related polyhedra

Great disdyakis triacontahedron

Great disdyakis triacontahedron
TypeStar polyhedron
Face
ElementsF = 120, E = 180
V = 62 (χ = 2)
Symmetry groupIh, [5,3], *532
Index referencesDU68
dual polyhedronGreat truncated icosidodecahedron

The great disdyakis triacontahedron is a nonconvex isohedral polyhedron. It is the dual of the great truncated icosidodecahedron.

See also

References

External links

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