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The regular polyhedra are those that have congruent and regular vertices, faces and edges. They are listed here, along with their Schläfli symbols.

Platonic Edit

The five Platonic solids are the convex regular polyhedra.

Kepler-Poinsot Edit

The four Kepler-Poinsot polyhedra are concave, intersect themselves, and some have star polygons as faces rather than convex ones.

Abstract Edit

Abstract polyhedra are topologically equivalent to tilings of hyperbolic space. Therefore, they are not considered part of the nine main regular polyhedra, but are listed nonetheless.

Spherical Edit

Spherical polyhedra can only exist on the surface of a sphere, and are degenerate in normal Euclidean space. Therefore, they are not considered part of the nine main regular polyhedra.