Let S be a rotation through angle , and let A_0 be any point not on the axis of S. Then the points  are the vertices of a regular polygon n whose sides are the segments A_0A_1, A_1A_2, ...

When n is an integer (greater than 2) this definition is equivalent to that given for regular polyhedra. But the polygon can be closed without n being integral; it is merely necessary that the period of S to be finite, i.e., that n be rational. We still stipulate that  since a positive rotation through an angle greater than Pi is the same as a negative rotation through an angle less than Pi.

To access the information relating to a regular star polygon p, use the following function calls:

The command with(geometry,RegularStarPolygon) allows the use of the abbreviated form of this command.