How to parameterize an orange peel I'm trying to parameterize the space curve determined by the boundary of a standard orange peel: for example, the one on this photo: !orange peel For example, the ideal curve would be inside the unit cube; have only one point of intersection with every horizontal plane $z=k$, when $k\in [-1,1]$; would start in $(0, 0, -1)$ and end in $(0, 0, 1)$, wrapping itself around them; and touch the boundary of the cube when $z=0$. It's sort of a standard helix, compressed. I hope I was clear.

Well, you seem to have a lot of options; there are a number of spherical spirals that would do. The loxodrome is one (the spherical analogue of the equiangular spiral), and Seiffert's spiral is another.