Squared Tori
A torus and the gluing instructions to create a torus from a square.
Topologically, the torus can be defined as the fundamental square [0,1] × [0,1] with its top and bottom sides identified by the relation (x, 0) ~ (x, 0) for 0 ≤ x ≤ 1, and left and right sides identified by the relation (y, 0) ~ (y, 0) for 0 ≤ y ≤ 1 as in the diagram on the right. To put it another way, it can be constructed from a rectangle by gluing both pairs of opposite edges together with no twists .
An (ordinary) torus is a surface having genus one, and therefore possessing a single "hole". The usual torus embedded in three-dimensional space is shaped like a donut.