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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.
For generalized cyclogons [1] and generalized trochoidal curves [2], 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.

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References
[1] T. M. Apostol and M. A. Mnatsukanian, "Generalized Cyclogons," Math Horizons, 2002 pp. 25–28. www.mamikon.com/USArticles/GenCycloGons.pdf.
[2] 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.
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