Is a polar geosynchronous orbit described by Viviani’s curve?

This answer to Is there a name for the great circle where latitude and longitude are equal? says (in part):

More generally, a clélie is the name given to any spherical curve where the longitude $\varphi$ and colatitude $\theta$ have the relationship $\varphi=c\theta,\quad c>0$, and the curve of Viviani corresponds to the locus of a geosynchronous orbit, $c=1$.

Is it really true that a polar geosynchronous orbit (displayed in a synodic or rotating frame) is described by Viviani's curve? Can this be demonstrated mathematically?

• Answers to Is an Earth synchronous (?) polar orbit possible? don't mention this,

• but this answer does show some similar-looking curves for geosynchronous orbits that are not polar.

Source