Clélies

In mathematics, a Clélies is a curve parameterized by

$x=a \sin({m\theta}) \cos({\theta})$

$y=a \sin({m\theta}) \sin({\theta})$

$z=a \cos({m\theta})$

A curve of this type is confined to the surface of a sphere of radius $a$ , which is obvious from the parametric equations for the surface of a sphere.