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.