Wider Scope: List of Polytopes by Type
Polyhedra are three-dimensional polytopes. They have vertices, edges, faces and a single cell.
Another name for Polyhedron is Polycubinaosias le Polytopana (A Wiki contributor)
Types[]
By Construction[]
- List of Rotatopic Polyhedra
- List of Prism Polyhedra - Polyhedra formed by extruding polygons into three dimensions
- List of Antiprism Polyhedra - Polyhedra formed by connecting two polygons using alternating triangles
- List of Regular Polyhedra - Polyhedra with congruent, regular faces and vertices
- List of Truncated Polyhedra - Polyhedra with vertices cut and replaced with faces
- List of Quasiregular Polyhedra - Polyhedra with two regular faces which alternate around each vertex
- List of Trapezivert Polyhedra
- List of Omnitruncated Polyhedra
- List of Snub Polyhedra
By Verf[]
- List of Polyhedra with Triangular Verfs (Verf: Triangle)
- List of Polyhedra with Square Verfs (Verf: Square)
- List of Polyhedra with Pentagonal Verfs (Verf: Pentagon)
- List of Polyhedra with Hexagonal Verfs (Verf: Hexagon)
- List of Polyhedra with Octagonal Verfs (Verf: Octagon)
List of Rotatopic Polyhedra[]
Rotatopic polyhedra are polyhedra formed from the product of multiple hyperspheres. There are exactly three rotatopic polyhedra, listed below along with their constituent hyperspheres (using Bowers' rotatope notation):
List of Prism Polyhedra[]
Full article: List of Prism Polyhedra
List of Antiprism Polyhedra[]
Antiprism polyhedra are formed by connecting two polygons through space with alternating triangles. Similar to the prism polyhedra, there are a countably infinite number of these.
Some significant antiprisms are:
- Tetrahedron (digon-based)
- Octahedron (triangle-based)
- Square Antiprism
- Pentagonal Antiprism
- Hexagonal Antiprism
- Heptagonal Antiprism
- Octagonal Antiprism
- Enneagonal Antiprism
- Decagonal Antiprism
List of Regular Polyhedra[]
Full article: List of Regular Polyhedra
List of Truncated Polyhedra[]
Full article: List of Truncated Polyhedra