Uniform star polyhedron

The remaining 10 nonprismatic uniform star polyhedra, those that pass through the center, are the hemipolyhedra as well as Miller's monster, and do not have well-defined densities.

An additional figure, the pseudo great rhombicuboctahedron, is usually not included as a truly uniform star polytope, despite consisting of regular faces and having the same vertices.

Note: For nonconvex forms below an additional descriptor nonuniform is used when the convex hull vertex arrangement has same topology as one of these, but has nonregular faces.

There is one nonconvex form, the tetrahemihexahedron which has tetrahedral symmetry (with fundamental domain Möbius triangle (3 3 2)).

truncated dodecahedron 3⁄2 | 3 5 Coxeter identified a number of degenerate star polyhedra by the Wythoff construction method, which contain overlapping edges or vertices.