This curve, with the form of the Greek capital delta, has been given also as names:

This quartic curve 1)  is the hypocycloid for which the rolled circle is three times as large as the rolling circle.
Given a tangent l to the curve. It cuts the curve in points P and Q. Then PQ has a length of 4, and the tangents to the curve in P and in Q make a right angle.
The length of the deltoid is 16, and the area it encloses: 2π.

Some other properties of the curve:

Three pedals of the curve are:

pedal point pedal curve
cusp simple folium
vertex double folium
center trifolium

The curve has been investigated as first by Leonhard Euler (1745), while studying an optical problem.


1) In Cartesian coordinates: (x2 + y2)2 -8x(x2 - 3y2) + 18(x2 + y2) = 27