Torus:

A torus is an orientable surface of genus one. That is, it is a sphere with one handle. It has Euler characteristic equal to 0.

Less formally, it is a surface in the shape of a bagel or doughnut. It can be made from a rectangular piece of plane by identifying the top and bottom edges (i.e., rolling it into a tube) and then identifying the left and right edges (that is, bending the tube around so that the ends meet).

An n-handled torus is a sphere with n handles; it has Euler characteristic equal to 2 - 2 n.

8/12/94 dpvc@geom.umn.edu -- The Geometry Center