List of Regular Polyhedra

The regular polyhedra are those that have congruent and regular vertices, faces and edges. They are listed here, along with their Schläfli symbols.
== Platonic ==
The five Platonic solids are the convex regular polyhedra.
* Tetrahedron \{3, 3\}
* Cube \{4, 3\}
* Dodecahedron \{5, 3\}
* Octahedron \{3, 4\}
* Icosahedron \{3, 5\}
== Kepler-Poinsot ==
The four Kepler-Poinsot polyhedra are concave, intersect themselves, and some have star polygons as faces rather than convex ones.
* Great Stellated Dodecahedron \{5/2, 3\}
* Great Icosahedron \{3, 5/2\}
* Great Dodecahedron \{5, 5/2\}
* Small Stellated Dodecahedron \{5/2, 5\}
== Abstract ==
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.
* Dodecadodecahedron \{5, 4\}
* Medial Rhombic Triacontahedron \{4, 5\}
* Medial Triambic Icosahedron \{6, 5\}
* Ditrigonal Dodecadodecahedron \{5, 6\}
* Excavated Dodecahedron \{6, 6\}
== Spherical ==
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 \{1, 1\}
* Henagonal Hosohedron \{2, 1\}
* Henagonal Dihedron \{1, 2\}
* Digonal Dihedron / Digonal Hosohedron \{2, 2\}
* Trigonal Hosohedron \{2, 3\}
* Trigonal Dihedron \{3, 3\}
Category:List of 3rd dimension