Nonconvex great rhombicosidodecahedron


In geometry, the nonconvex great rhombicosidodecahedron is a nonconvex uniform polyhedron, indexed as U67. It has 62 faces, 120 edges, and 60 vertices. It is also called the quasirhombicosidodecahedron. It is given a Schläfli symbol t0,2. 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 = /2 is the golden ratio.

Related polyhedra

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, and the great rhombidodecahedron.

Nonconvex great rhombicosidodecahedron
Great dodecicosidodecahedron
Great rhombidodecahedron

Truncated great dodecahedron
Compound of six pentagonal prisms
Compound of twelve pentagonal prisms

Great deltoidal hexecontahedron

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.
It is also called a great strombic hexecontahedron.