List of uniform polyhedra by Wythoff symbol
From Wikipedia, the free encyclopedia
| Polyhedron | |
| Class | Number and properties |
|---|---|
| Platonic solids |
(5, convex, regular) |
| Archimedean solids |
(13, convex, uniform) |
| Kepler–Poinsot polyhedra |
(4, regular, non-convex) |
| Uniform polyhedra |
(75, uniform) |
| Prismatoid: prisms, antiprisms etc. |
(4 infinite uniform classes) |
| Polyhedra tilings | (11 regular, in the plane) |
| Quasi-regular polyhedra |
(8) |
| Johnson solids | (92, convex, non-uniform) |
| Bipyramids | (infinite) |
| Pyramids | (infinite) |
| Stellations | Stellations |
| Polyhedral compounds | (5 regular) |
| Deltahedra | (Deltahedra, equilateral triangle faces) |
| Snub polyhedra |
(12 uniform, not mirror image) |
| Zonohedron | (Zonohedra, faces have 180°symmetry) |
| Dual polyhedron | |
| Self-dual polyhedron | (infinite) |
| Catalan solid | (13, Archimedean dual) |
There are many relations among the uniform polyhedra.
Here they are grouped by the Wythoff symbol.
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Image |
Regular
All the faces are identical, each edge is identical and each vertex is identical. They all have a Wythoff symbol of the form p|q 2.
Convex
The Platonic solids.
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Non-convex
The Kepler-Poinsot solids.
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Quasi-regular
Each edge is identical and each vertex is identical. There are two types of faces which appear in an alternating fashion around each vertex. The first row are semi-regular with 4 faces around each vertex. They have Wythoff symbol 2|p q. The second row are ditrigonal with 6 faces around each vertex. They have Wythoff symbol 3|p q or 3/2|p q.
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