| 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 |
| Symmetry group | Oh, [4,3], *432 |
| Index references | U17, C59, W85 |
| Bowers acronym | Querco |
4.4.4.3/2 (Vertex figure) |
Great deltoidal icositetrahedron (dual polyhedron) |
In geometry, the nonconvex great rhombicuboctahedron is a nonconvex uniform polyhedron, indexed as U17. It is represented by Schläfli symbol t0,2{4,3/2} 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.
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).
Truncated cube |
Nonconvex great rhombicuboctahedron |
Great cubicuboctahedron |
Great rhombihexahedron |