The Torus

The Torus is obtained by identifying the opposite edges of a square. This manifold is often described as the "surface of a doughnut". If one wanted to make a doughnut out of a piece of paper, one would first roll the paper into a tube, perhaps gluing the top edge to the bottom edge -- this "gluing" is what is meant by the phrase "identifying opposite edges". Of course with real paper, it would be difficult to accomplish the second identification, but we can imagine some sort of nice rubbery material that would allow us to glue first in one direction (making a tube) and then in the other direction (bending the tube around to make a doughnut)

This animation (which should be familiar to video game addicts) shows the dynamics of life in a toroidal universe.