People have played with explicitly parametrized surfaces to produce shapes like the
or many others. One does not get closed surfaces of higher genus that way. Implicitly defined
closed surfaces are easily obtained with high genus. This animation is one of the simplest examples:
multiply two functions which each have an ellipse as minimum set and vary the distance of the
two ellipses. —
Join of 2 Tori
Bretzel5 Implicit Surface
are similar examples.