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}
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 is a nonconvex uniform polyhedron, indexed as U₆₈. It is given a Schläfli symbol t_0,1,2{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
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

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

See also

• List of uniform polyhedra

References

• Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 730208 p. 96

External links

• Weisstein, Eric W., "Great truncated icosidodecahedron", MathWorld.
• Weisstein, Eric W., "Great disdyakis triacontahedron", MathWorld.