Define a "ring" as a grouping of congruent regular polygons, each sharing a side with two others, made into a fully rotationally symmetrical ring. That is, it has as many rotational symmetries as there are polygons.

For example, 6 equilateral triangles can be made into a very tight ring, as can 4 squares or 3 regular hexagons. Ten regular pentagons can also be made into a ring with a nice decagon inside. For hexagons, there can also be a ring of 6 with a central hexagon. The central region need not be a regular polygon.

The "Ring Set" R(n) is the set of possible numbers of n-gons that can make a ring.

From the above examples, R(3)={6}, R(4)={4}, R(5)={10} and R(6)={3,6}. Find a rule to describe R(n).