Before we start this is a Torus.
It's a three dimensional shape with only one face (a bit like a sphere).
In Torus Games (free) you can play all sorts of games such as noughts and crosses, pool, 5-in-a-row but with the added twist that the board is torus shaped so has no edges. Therefore you can win noughts and crosses like this:
It's also possible to change the settings and play the game on a Klein bottle: