in mathematics, in geometry, a cyclogon is the curve traced by a vertex of a polygon that rolls without slipping along a straight line. there are no restrictions on the nature of the polygon. it can be a regular polygon like an equilateral triangle or a square. the polygon need not even be convex: it could even be a star-shaped polygon. more generally, the curves traced by points other than vertices have also been considered. in such cases it would be assumed that the tracing point is rigidly attached to the polygon. if the tracing point is located outside the polygon, then the curve is called a "prolate cyclogon", and if it lies inside the polygon it is called a "curtate cyclogon".