Semi-Regular Polyhedron

A polyhedron is said to be semi-regular if it is not a regular polyhedron, but:

  1. All it's faces are regular polygons;
  2. The same sequence of polygons surrounds each vertex.

There are two trivial infinite sets of semi-regular polyhedra: the set of archimedean prisms (those with regular bases and square sides); and the set of archimedean antiprisms (those with regular bases and equilateral triangular sides). In addition, there are just thirteen more convex semi-regular polyhedra. These are know as the archimedean solids. Allowing non-convex or star polyhedra, there are additional more semi-regular solids, known as the stellated archimedeans. The exact size of this catagory depends on the precise restrictions made.