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

Great hexacronic icositetrahedron

The great hexacronic icositetrahedron is the dual of the great cubicuboctahedron.