Great truncated icosidodecahedron

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Great truncated icosidodecahedron
Type	Uniform polyhedron
Elements	F=62, E=180, V=120 (χ=2)
Faces by sides	30{4}+20{6}+12{10/3}
Wythoff symbol	2 35/3 |
Symmetry group	Ih
Index references	U68, C87, W108
4.6.10/3 (Vertex figure)	Great disdyakis triacontahedron (dual polyhedron)

In geometry, the great truncated icosidodecahedron is a nonconvex uniform polyhedron, indexed as U₆₈.

[edit] 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.

[edit] See also

• List of uniform polyhedra

[edit] External links

• Eric W. Weisstein, Great truncated icosidodecahedron at MathWorld.