Snub polyhedra
A snub polyhedron is a polyhedron obtained by alternating a corresponding omnitruncated or truncated polyhedron, depending on the definition. Some but not all authors include antiprisms as snub polyhedra, as they obtained by this construction from a degenerate "polyhedron" with only two faces.
Chiral snub polyhedra do not always have reflection symmetry and hence sometimes have two enantiomorphous forms which are reflections of each other. Their symmetry groups are all point groups.
For example, the snub cube:
Snub polyhedra have Wythoff symbol | p q r and by extension, vertex configuration 3.p.3.q.3.r. Retrosnub polyhedra (a subset of the snub polyhedron, containing the great icosahedron, small retrosnub icosicosidodecahedron, and great retrosnub icosidodecahedron) still have this form of Wythoff symbol, but their vertex configurations are instead (3.−p.3.−q.3.−r)/2.
Among the snub polyhedra that cannot be otherwise generated, only the pentagonal antiprism, pentagrammic antiprism, pentagrammic crossed-antiprism, small snub icosicosidodecahedron and small retrosnub icosicosidodecahedron are known to occur in any non-prismatic uniform 4-polytope. The tetrahedron, octahedron, icosahedron, and great icosahedron appear commonly in non-prismatic uniform 4-polytopes, but not in their snub constructions. Every snub polyhedron however can appear in the polyhedral prism based on them.
...
Wikipedia