Snub (geometry)
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Two snub cubes from great rhombicuboctahedron
See that red and green dots are placed at alternate vertices. A snub cube is generated from deleting either set of vertices, one resulting in clockwise gyrated squares, and other counterclockwise.
A snub is an operation on a polyhedron which fully truncates alternate vertices. Only zonohedra can have this operation performed so every 2n-sided face becomes n-sided.
A snubbed regular polyhedron is generated in two steps. First a regular polyhedron is omnitruncated. This creates a vertex configuration 4.2p.2q. Then this form is snubbed. The squares become degenerated into edges, and new triangle faces form at each original vertex, creating vertex configuration 3.3.p.3.q.
A snub operations has two choices of vertices and so for some polyhedra, it can create two chiral forms.
Non-uniform zonohedra can also snubbed. For instance, the Rhombic triacontahedron can be snubbed into either an icosahedron or a dodecahedron depending on which vertices are rectified.
Examples
Platonic solid generators
Three steps: regular --> omnitruncated --> snubbed
| Symmetry | Regular | Omnitruncated | Snub |
|---|---|---|---|
| Tetrahedral (3 3 2) |  Tetrahedron |  truncated octahedron |  icosahedron |
| Octahedral (4 3 2) |  Cube |  Great rhombicuboctahedron |  snub cube |
| Icosahedral (5 3 2) |  Dodecahedron |  Great rhombicosidodecahedron |  snub dodecahedron |
Regular tiling generators
| Symmetry | Regular | Omnitruncated | Snub |
|---|---|---|---|
| Square (4 4 2) |  (4.4.4.4) |  (4.8.8) |  (3.3.4.3.4) |
| Hexagonal (6 3 2) |  (6.6.6) |  (3.4.6.4) |  3.3.3.3.6 |
Uniform prism generators (dihedral symmetry)
Two steps: 2n-gonal prisms --> n-gonal antiprism.
- # cube --> tetrahedron
- #*
--> 
- # hexagonal prism --> octahedron
- #*
--> 
- # octagonal prism --> square antiprism
- #*
--> 
- # decagonal prism --> pentagonal antiprism
- #*
--> 
- # ....
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