Lissajous-toric knot

In knot theory, a Lissajous-toric knot is a knot defined by parametric equations of the form:

${\displaystyle x(t)=(2+\sin qt)\cos Nt,\qquad y(t)=(2+\sin qt)\sin Nt,\qquad z(t)=\cos p(t+\phi ),}$

where ${\displaystyle N}$, ${\displaystyle p}$, and ${\displaystyle q}$ are integers, the phase shift ${\displaystyle \phi }$ is a real number and the parameter ${\displaystyle t}$ varies between 0 and ${\displaystyle 2\pi }$.

For ${\displaystyle p=q}$ the knot is a torus knot.