The roulette traced by a point attached to the polygon consists of two different curve types:

1. involute curve sections when an edge of the polygon rolls tangentially over the base circle.

2. circle arcs when a vertex of the polygon makes contact with the base circle.

Varying the circumradius of the rolling polygon changes the circumference ratio between the polygon and the base circle.

A closed curve can be obtained after one revolution around the base circle if the circumference of the -sided regular polygon equals .

By increasing the number of vertices of the polygon, the trace approaches an epitrochoid.