Swastika curve

The plane curve with the Cartesian equation

${\displaystyle y^{4}-x^{4}=xy,\,}$

or, equivalently, the polar equation

${\displaystyle r^{2}={\frac {\sin(\theta )\cos(\theta )}{\sin ^{4}(\theta )-\cos ^{4}(\theta )}}=-{\frac {\tan(2\theta )}{2}}.\,}$

The curve looks similar to the right-handed swastika. It can be inverted with respect to a unit circle to resemble a left-handed swastika. The Cartesian equation then becomes a quartic curve,

${\displaystyle x^{4}-y^{4}=xy.\,}$

• "Swastika Curve". Mathworld.