Pseudo-uniform polytope

A pseudo-uniform polytope is a polytope whose facets are all uniform and whose vertex figures are congruent (i.e. the same configuration of facets meets at each vertex), but is not itself vertex transitive and therefore fails to be uniform.

There are two known pseudo-uniform polyhedra: the elongated square gyrobicupola (or pseudorhombicuboctahedron, a Johnson solid) and the great pseudorhombicuboctahedron. It is not known if there are any others.