A regular skew polyhedron, in the classical Coxeter-Petrie terminology, is an infinite regular polyhedron in Euclidean
space with planar regular polygon faces
and regular skew polygons as vertex
figures. In modern terminology, such a polyhedron is a regular skew apeirohedron.
There are exactly three in three-dimensional Euclidean
space: 
,
,
and 
(Coxeter 1937).
Garner (1967) considered regular skew polyhedra in hyperbolic space 
and found 32 associated with honeycombs whose cells
and vertex figures are not inscribed in equidistant
surfaces.
