Roulette (Epitrochogon) of a Disk Rolling around a Regular Polygon
This Demonstration simulates a circle rolling without slipping on the outside of a stationary regular polygon of circumradius 1. A point is attached to the circle; its trace is called an epitrochogon.[more]
For generalized cyclogons  and generalized trochoidal curves , these roulettes can be considered a limiting case of epitrochogons with an infinite number of vertices of the rolling polygon.
These epitrochogons consist of sequences of two distinct curve types, each generated by a different type of motion:
1. a cycloidal or rolling motion of the circle along the straight edges of the polygon.
2. a circular motion when turning around the vertices of the polygon.[less]
 T. M. Apostol and M. A. Mnatsukanian, "Generalized Cyclogons," Math Horizons, 2002 pp. 25–28. www.mamikon.com/USArticles/GenCycloGons.pdf.
 T. M. Apostol and M. A. Mnatsukanian, "Area & Arc Length of Trochogonal Arches," Math Horizons, 2003 pp. 24–30. www.mamikon.com/USArticles/TrochoGons.pdf.
"Roulette (Epitrochogon) of a Disk Rolling around a Regular Polygon"
Wolfram Demonstrations Project
Published: December 8 2016