In geometry, a cyclogon is the curve traced by a vertex of a regular polygon that rolls without slipping along a straight line.
[1][2] In the limit, as the number of sides increases to infinity, the cyclogon becomes a cycloid.
A cyclogon is obtained when a polygon rolls over a straight line.
In this more general situation, let a curve be traced by a point z on a regular polygonal disk with n sides rolling around another regular polygonal disk with m sides.
A point z attached rigidly to the n-gon traces out an arch consisting of n circular arcs before repeating the pattern periodically.
Animation showing the generation of one arch of a cyclogon by an equilateral triangle as the triangle rolls over a straight line without slipping.
Animation showing the generation of one arch of a cyclogon by a square as the square rolls over a straight line without slipping.
Animation showing the tracing of a prolate cyclogon as an equilateral triangle rolls over a straight line without skipping. The tracing point X is outside the disk of the triangle.
Animation showing the tracing of a curtate cyclogon as an equilateral triangle rolls over a straight line without skipping. The tracing point Y is inside the disk of the triangle.
