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
(x2 + y2)2 - 8ax(x2 - 3y2) + 18a2(x2 + y2) = 27a4.