Snub polyhedron

In geometry, a snub polyhedron is a polyhedron obtained by performing a snub operation: alternating a corresponding omnitruncated or truncated polyhedron, depending on the definition. Some, but not all, authors include antiprisms as snub polyhedra, as they are obtained by this construction from a degenerate "polyhedron" with only two faces (a dihedron). Chiral snub polyhedra do not always have reflection symmetry and hence sometimes have two enantiomorphous (left- and right-handed) forms which are reflections of each other. Their symmetry groups are all point groups. For example, the snub cube: Snub polyhedra have Wythoff symbol p q r and by extension, vertex configuration 3.p.3.q.3.r. Retrosnub polyhedra (a subset of the snub polyhedron, containing the great icosahedron, small retrosnub icosicosidodecahedron, and great retrosnub icosidodecahedron) still have this form of Wythoff symbol, but their vertex configurations are instead \frac{(3.-p.3.-q.3.-r)}{2}. There are 12 uniform snub polyhedra, not including the antiprisms, the icosahedron as a snub tetrahedron, the great icosahedron as a retrosnub tetrahedron and the great disnub dirhombidodecahedron, also known as Skilling's figure. When the Schwarz triangle of the snub polyhedron is isosceles, the snub polyhedron is not chiral. This is the case for the antiprisms, the icosahedron, the great icosahedron, the small snub icosicosidodecahedron, and the small retrosnub icosicosidodecahedron. In the pictures of the snub derivation (showing a distorted snub polyhedron, topologically identical to the uniform version, arrived at from geometrically alternating the parent uniform omnitruncated polyhedron) where green is not present, the faces derived from alternation are coloured red and yellow, while the snub triangles are blue. Where green is present (only for the snub icosidodecadodecahedron and great snub dodecicosidodecahedron), the faces derived from alternation are red, yellow, and blue, while the snub triangles are green.