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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, .
Contents
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.
Great disdyakis triacontahedron
The great disdyakis triacontahedron is a nonconvex isohedral polyhedron. It is the dual of the great truncated icosidodecahedron.
References
Great truncated icosidodecahedron Wikipedia(Text) CC BY-SA