# Nonconvex great rhombicosidodecahedron

(Redirected from Quasirhombicosidodecahedron)
Nonconvex great rhombicosidodecahedron
Type Uniform star polyhedron
Elements F = 62, E = 120
V = 60 (χ = 2)
Faces by sides 20{3}+30{4}+12{5/2}
Wythoff symbol 5/3 3 | 2
5/2 3/2 | 2
Symmetry group Ih, [5,3], *532
Index references U67, C84, W105
Dual polyhedron Great deltoidal hexecontahedron
Vertex figure
3.4.5/3.4
Bowers acronym Qrid

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

Cartesian coordinates for the vertices of a nonconvex great rhombicosidodecahedron are all the even permutations of

(±1/τ2, 0, ±(2−1/τ))
(±1, ±1/τ3, ±1)
(±1/τ, ±1/τ2, ±2/τ)

where τ = (1+√5)/2 is the golden ratio (sometimes written φ).

## 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 (having the triangular and pentagrammic faces in common), and the great rhombidodecahedron (having the square faces in common).

 Nonconvex great rhombicosidodecahedron Great dodecicosidodecahedron Great rhombidodecahedron Truncated great dodecahedron Compound of six pentagonal prisms Compound of twelve pentagonal prisms

### Great deltoidal hexecontahedron

Great deltoidal hexecontahedron
Type Star polyhedron
Face
Elements F = 60, E = 120
V = 62 (χ = 2)
Symmetry group Ih, [5,3], *532
Index references DU67
dual polyhedron Nonconvex great rhombicosidodecahedron

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.