skew polyhedron

A regular skew polyhedron is a polyhedron whose faces and vertex figures are regular skew polygons. There are only three regular skew polyhedra in Euclidean three-space, the simplest of which is {4, 6|4}. Garner considered regular skew polyhedra in hyperbolic space H^3, and shows that there are exactly 32 which are derived from honeycombs whose cells and vertex figures are derived from honeycombs whose cells and vertex figures are not inscribed in equidistant surfaces.