A good deal of work has been done on polychoral torii. It's quite interesting.
There are toratopes, to which a whole subforum
viewforum.php?f=24 is given to. There are things called tigers, which are interesting too. Keiji has done a good deal of work here.
There's a comb product, which is the 'repetition of surfaces'. One use of this is to produce 'polytope torus skins'.
In four dimensions, the skin of a polytope is 3d. So if you take a 2d skin (say a dodecahedron), and a 1d skin (say a decagon), you can multiply these in cartesian product to get a 3d skin which covers two different torii.
Suppose you take a hollow dodecahedron (ie its skin), and take a prism-product of a ten-link chain (say a decagon-skin). You then have a kind of pipe in 4d, like a dodecahedral prism stack, ten high, with the dodecahedra blown out: in effect, you have 120 pentagonal prisms.
You can join top to bottom in the 'hose' fashion, by bending the tower around in a C fashion, and then link top to bottom. What's inside the pipe will end up inside the torus.
You can join top to bottom in the 'sock' fashion. What this does, is you make the top bigger, and roll it down the pipe, rather as you might roll a sock down your leg. When the top gets to the bottom, you then join it. What's inside the sock ends up outside the torus.
You can make a 3d skin out of three 1D skins, so what you get is a torus whose section is a torus. You take a 3d rectanguloid of rubbery cubes, and you roll it into a cylinder, and then the top to bottom into a torus. So you have a torus-shaped pipe. Which ever way you do it, sock or hose, you end up with the same figure.