Nonconvex great rhombicosidodecahedron
In geometry, the nonconvex great rhombicosidodecahedron is a nonconvex uniform polyhedron, indexed as U67. It is also called the quasirhombicosidodecahedron. It is given a Schläfli symbol t0,2{5/3,3}. Its vertex figure is a crossed quadrilateral.
This model shares the name with the convex great rhombicosidodecahedron, also known as the truncated icosidodecahedron.
Cartesian coordinates for the vertices of a nonconvex great rhombicosidodecahedron are all the even permutations of
where τ = (1+√5)/2 is the golden ratio (sometimes written φ).
It shares its vertex arrangement with the truncated great dodecahedron, and with the uniform compounds of 6 or 12 pentagonal prisms. It additionally shares its edge arrangement with the great dodecicosidodecahedron (having the triangular and pentagrammic faces in common), and the great rhombidodecahedron (having the square faces in common).
The great deltoidal hexecontahedron is a nonconvex isohedral polyhedron. It is the dual of the nonconvex great rhombicosidodecahedron. It is visually identical to the Great rhombidodecacron. It has 60 intersecting cross quadrilateral faces, 120 edges, and 62 vertices.
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