- All it's faces are regular polygons;
- 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.