Quadrifolium

The quadrifolium is a type of rose curve with n=2. It has polar equation:

r = acos(2θ),

with corresponding algebraic equation

(x² + y²)³ = a2(x² − y²)²

Rotated by 45°, this becomes

r = asin(2θ)

with corresponding algebraic equation

(x² + y²)³ = 4ax²y² .

In either form, it is a plane algebraic curve of genus zero.