Read the

hypocycloid writeup first. The

deltoid is a

plane algebraic curve. It is the hypocycloid such that the

radius of the fixed

circle is 3 times the radius of the rolling circle,

*a* say.
It looks like a

triangle where the edges of the triangle have been
curved toward the centre.

An equation for the deltoid is

*
(x*^{2} + y^{2})^{2} - 8ax(x^{2} - 3y^{2}) + 18a^{2}(x^{2} + y^{2}) = 27a^{4}.