After seeing the umbilical torus statue at the Beckman Institue at the University of Illinois, we resolved to make one. The mathematical description (see http://en.wikipedia.org/wiki/Umbilic_torus) did not easily yield a printable surface, so we modeled it as a rotating triangle in OpenSCAD. The attached code does the equivalent of a rotate_extrude command, with a spinning 2D triangle.

The OpenSCAD file is parameterized to make it easy to change the radius and size of the triangle.

The STL file may need to be scaled up to your desired size. It was printed with .2 layers using Makerware with support and raft.