Star polyhedron

While degenerate in Euclidean space, they can be realised spherically in nondegenerate form.

There are many uniform star polyhedra including two infinite series, of prisms and of antiprisms, and their duals.

For example, the complete stellation of the icosahedron (illustrated) can be interpreted as a self-intersecting polyhedron composed of 20 identical faces, each a (9/4) wound polygon.

For example, the great grand stellated 120-cell, projected orthogonally into 3-space, looks like this: There are no regular star polytopes in dimensions higher than 4[citation needed].

For instance, the small stellated dodecahedron has 12 pentagram faces, but the corresponding star domain has 60 isosceles triangle faces, and correspondingly different numbers of vertices and edges.

Polyhedral star domains appear in various types of architecture, usually religious in nature.