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*