Elongated retrograde square gyrobicupola

The pseudo great rhombicuboctahedron is one of the two known pseudo-uniform polyhedra, the other being the elongated square gyrobicupola or pseudorhombicuboctahedron. All its faces are regular and the same configuration of faces meet at each vertex, but it is not isogonal. This is because the vertices divide into two sets, one of size 16 and the other of size 8, that are distinct according to the symmetries of the polyhedron.

The pseudo great rhombicuboctahedron is the result of starting with a quasirhombicuboctahedron (sometimes called the "great rhombicuboctahedron," but regrettably there is a different polyhedron often called that) and gyrating a retrograde square cupola by 45 degrees. This breaks up four of the quasirhombicuboctahedron's six octagrammic pseudo-faces.