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)
Contents
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
