Nonconvex great rhombicuboctahedron
In geometry, the nonconvex great rhombicuboctahedron is a nonconvex uniform polyhedron, indexed as U17. It has 26 faces, 48 edges, and 24 vertices. It is represented by Schläfli symbol t0,2 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.
Orthogonal projections
Cartesian coordinates
for the vertices of a nonconvex great rhombicuboctahedron centered at the origin with edge length 1 are all the permutations ofwhere ξ = − 1.
Related polyhedra
It shares the vertex arrangement with the convex truncated cube. It additionally shares its edge arrangement with the great cubicuboctahedron, and with the great rhombihexahedron. 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 |