A mathematical construct specified by a pair of parametric equations. Specific case of the more generic cyclohedron. Related 2D forms include hypercycloid and curtate cycloid, which are also generalizations.

For a cycloid based on a circle of radius r with rotation angle a, the parametric equations are as follows:


An interesting property of this construct is that the area under the first dome-shape (a=0 to a=2pi) is equal to 8r.