The five Platonic solids are the convex regular polyhedra.
The four Kepler-Poinsot polyhedra are concave, intersect themselves, and some have star polygons as faces rather than convex ones.
- Great Stellated Dodecahedron
- Great Icosahedron
- Great Dodecahedron
- Small Stellated Dodecahedron
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.
- Medial Rhombic Triacontahedron
- Medial Triambic Icosahedron
- Ditrigonal Dodecadodecahedron
- Excavated Dodecahedron
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.
- Henagonal Henahedron
- Henagonal Hosohedron
- Henagonal Dihedron
- Digonal Dihedron / Digonal Hosohedron
- Trigonal Hosohedron
- Trigonal Dihedron