Alternation (geometry)

Alternation (geometry)

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.

In geometry, an alternation (also called partial truncation, snub or snubification) is an operation on a polyhedron or tiling that removes alternate vertices. Only even-sided polyhedra can be alternated, for example the zonohedra. Every 2n-sided face becomes n-sided. Square faces disappear into new edges.

An alternation of a regular polyhedron or tiling is sometimes labeled by the regular form, prefixed by an h, standing for half. For example h{4,3} is an alternated cube (creating a tetrahedron), and h{4,4} is an alternated square tiling (still a square tiling).