a cyclogon is obtained when a polygon rolls over a straight line. let it be assumed that the regular polygon rolls over the edge of another polygon. let it also be assumed that the tracing point is not a point on the boundary of the polygon but possibly a point within the polygon or outside the polygon but lying in the plane of the polygon. 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. the edges of the two regular polygons are assumed to have the same length. a point z attached rigidly to the n-gon traces out an arch consisting of n circular arcs before repeating the pattern periodically. this curve is called a trochogon — an "epitrochogon" if the n-gon rolls outside the m-gon, and a "hypotrochogon" if it rolls inside the m-gon. the trochogon is curtate if z is inside the n-gon, and prolate (with loops) if z is outside the n-gon. if z is at a vertex it traces an epicyclogon or a hypocyclogon.