A

David

Darling

nonconvex uniform polyhedron

small snub icosicosidodecahedron

Small snub icosicosidodecahedron.


A nonconvex uniform polyhedron is a uniform polyhedron of a type obtained by relaxing the conditions used to produce the Archimedean solids (which have regular convex faces and identical convex vertices) to allow both nonconvex faces and vertex types, as in the case of the Kepler-Poinset solids. The condition that every vertex must be identical, but the faces need not be, gives rise to 53 nonconvex uniform polyhedra. An example is the great truncated dodecahedron, obtained by truncating the corners of the great dodecahedron at a depth which gives regular decagons.