Quasiregular polyhedron
In geometry, a quasiregular polyhedron is a semiregular polyhedron that has exactly two kinds of regular faces, which alternate around each vertex. They are edge-transitive and hence a step closer to regular polyhedra than the semiregular which are merely vertex-transitive.
There are only two convex quasiregular polyhedra, the cuboctahedron and the icosidodecahedron. Their names, given by Kepler, come from recognizing their faces contain all the faces of the dual-pair cube and octahedron, in the first, and the dual-pair icosahedron and dodecahedron in the second case.
These forms representing a pair of a regular figure and its dual can be given a vertical Schläfli symbol or r{p,q} to represent their containing the faces of both the regular {p,q} and dual regular {q,p}. A quasiregular polyhedron with this symbol will have a vertex configuration p.q.p.q (or (p.q)2).
...
Wikipedia