Snub polyhedron
From Wikipedia, the free encyclopedia
| Polyhedron | |
| Class | Number and properties |
|---|---|
| Platonic solids |
(5, convex, regular) |
| Archimedean solids |
(13, convex, uniform) |
| Kepler-Poinsot solids |
(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, equalatial 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) |
A snub polyhedron is a polyhedron obtained by adding extra triangles around each vertex.
Chiral snub polyhedra do not have reflection symmetry and hence have two enantiomorphous forms which are reflections of each other. Their symmetry groups are all point groups and are one of:
- O - chiral octahedral symmetry;the rotation group of the cube and octahedron; order 24.
- I - chiral icosahedral symmetry; the rotation group of the icosahedron and the dodecahedron; order 60.
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The reflexible snub polyhedron where two polygons share the same the same facial planes. They have reflection symmetry across these planes and symmetry group Ih.
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[edit] Nonuniform snubs
Two of the Johnson solids are also called snubs: the snub disphenoid (symmetry group D2d) and the snub square antiprism (symmetry group D4d). Each is formed by splitting a polyhedron in two (along existing edges) and filling the gap with triangles. Neither is chiral.
