Great stellated truncated dodecahedron

In geometry, the great stellated truncated dodecahedron (or quasitruncated great stellated dodecahedron or great stellatruncated dodecahedron) is a nonconvex uniform polyhedron, indexed as U66.

It has 32 faces (20 triangles and 12 decagrams), 90 edges, and 60 vertices.

[1] It is given a Schläfli symbol t0,1{5/3,3}.

It shares its vertex arrangement with three other uniform polyhedra: the small icosicosidodecahedron, the small ditrigonal dodecicosidodecahedron, and the small dodecicosahedron: Cartesian coordinates for the vertices of a great stellated truncated dodecahedron are all the even permutations of

φ ,

{\displaystyle {\begin{array}{crclc}{\Bigl (}&0,&\pm \,\varphi ,&\pm {\bigl [}2-{\frac {1}{\varphi }}{\bigr ]}&{\Bigr )}\\{\Bigl (}&\pm \,\varphi ,&\pm \,{\frac {1}{\varphi }},&\pm \,{\frac {2}{\varphi }}&{\Bigr )}\\{\Bigl (}&\pm \,{\frac {1}{\varphi ^{2}}},&\pm \,{\frac {1}{\varphi }},&\pm \,2&{\Bigr )}\end{array}}}

is the golden ratio.

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