The torus:

This is obtained by identifying the opposite sides of the square $ I^2$ according to the following scheme. For each $ x \in [0, 1]$, the pair of points $ (x, 0)$ and $ (x, 1)$ are identified. Likewise for each $ y \in [0, 1]$ the pair of points $ (0, y)$ and $ (1, y)$ are identified. One first obtains a cylinder $ S^1 \times [0, 1]$ which is then ``bent around'' and the circular ends are glued together. One obtains a space which looks like the crust of a dough-nut (or medu vada).

nisha 2012-03-20