List of rotational symmetry polyhedral sets

There are an unlimited number of polyhedral sets which can be defined with rotational symmetry.

This list shows the some of the simplest sets which appear within the convex uniform polyhedra, Johnson solids and related duals.

Each set has one polyhedron for each polygon, and each is prefixed by its generating polygon: triangular, square, pentagonal, hexagonal, etc. Some have degenerate (linear) forms as well where the symmetry has collapsed to an edge.

There are three symmetry classes:

1. C_nv - n-fold pyramidal symmetry
2. D_nh - n-fold prismatic symmetry
3. D_nv - n-fold antiprismatic symmetry