Great cubicuboctahedron
In geometry, the great cubicuboctahedron is a nonconvex uniform polyhedron, indexed as U14. It has 20 faces, 18 edges, and 24 vertices. Its square faces and its octagrammic faces are parallel to those of a cube, while its triangular faces are parallel to those of an octahedron: hence the name cubicuboctahedron. The great suffix serves to distinguish it from the small cubicuboctahedron, which also has faces in the aforementioned directions.
Orthographic projections
Related polyhedra
It shares the vertex arrangement with the convex truncated cube and two other nonconvex uniform polyhedra. It additionally shares its edge arrangement with the nonconvex great rhombicuboctahedron, and with the great rhombihexahedron.Truncated cube | Nonconvex great rhombicuboctahedron | Great cubicuboctahedron | Great rhombihexahedron |