List of uniform polyhedra by vertex figure
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There are many relations among the uniform polyhedra.[1][2][3] Some are obtained by truncating the vertices of the regular or quasi-regular polyhedron. Others share the same vertices and edges as other polyhedron. The grouping below exhibit some of these relations.
More information Class, Number and properties ...
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) |
Pyramids and Bipyramids | (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) |
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