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:

**x=r(a-sin(a))**

y=r(1-cos(a))
An interesting

property of this construct is that the

area under the first

dome-shape (a=0 to a=2

pi) is equal to 8r.