Great rhombihexahedron

It shares the vertex arrangement with the convex truncated cube.

It additionally shares its edge arrangement with the nonconvex great rhombicuboctahedron (having 12 square faces in common), and with the great cubicuboctahedron (having the octagrammic faces in common).

Similarly, the small rhombihexahedron may be constructed as the exclusive or of three octagonal prisms.

The great rhombihexacron is a nonconvex isohedral polyhedron.

As a surface geometry, it can be seen as visually similar to a Catalan solid, the disdyakis dodecahedron, with much taller rhombus-based pyramids joined to each face of a rhombic dodecahedron.