# Nonconvex great rhombicuboctahedron

Nonconvex great rhombicuboctahedron Type Uniform star polyhedron
Elements F = 26, E = 48
V = 24 (χ = 2)
Faces by sides 8{3}+(6+12){4}
Wythoff symbol 3/2 4 | 2
3 4/3 | 2
Symmetry group Oh, [4,3], *432
Index references U17, C59, W85
Dual polyhedron Great deltoidal icositetrahedron
Vertex figure 4.4.4.3/2
Bowers acronym Querco

In geometry, the nonconvex great rhombicuboctahedron is a nonconvex uniform polyhedron, indexed as U17. It has 26 faces (8 triangles and 18 squares), 48 edges, and 24 vertices. It is represented by Schläfli symbol t0,2{4,​32} and Coxeter-Dynkin diagram of       . Its vertex figure is a crossed quadrilateral.

This model shares the name with the convex great rhombicuboctahedron, also called the truncated cuboctahedron.

An alternate name for this figure is quasirhombicuboctahedron. From that derives its Bowers acronym: querco.

## Cartesian coordinates

Cartesian coordinates for the vertices of a nonconvex great rhombicuboctahedron centered at the origin with edge length 1 are all the permutations of

ξ, ±1, ±1),

where ξ = 2 − 1.

## Related polyhedra

It shares the vertex arrangement with the convex truncated cube. It additionally shares its edge arrangement with the great cubicuboctahedron (having the triangular faces and 6 square faces in common), and with the great rhombihexahedron (having 12 square faces in common). It has the same vertex figure as the pseudo great rhombicuboctahedron, which is not a uniform polyhedron. Truncated cube Great rhombicuboctahedron Great cubicuboctahedron Great rhombihexahedron Pseudo great rhombicuboctahedron

### Great deltoidal icositetrahedron

Great deltoidal icositetrahedron

Type Star polyhedron
Face
Elements F = 24, E = 48
V = 26 (χ = 2)
Symmetry group Oh, [4,3], *432
Index references DU17
dual polyhedron Nonconvex great rhombicuboctahedron

The great deltoidal icositetrahedron is the dual of the nonconvex great rhombicuboctahedron.