Klein bottle

[Gonzolo]

I understand a Klein bottle is somewhat of a 3D version of a mobius strip in that it has only one continuous surface. But what do mathematicians do with it? How is it expressed mathematically, how does it classify among other shapes? Does it have some kind of applications?

[Gokul43201]

Ummm...I know it has an Euler characterstic of 0. But other than that ...

Yes, that seems to be correct; here's more : http://mathworld.wolfram.com/KleinBottle.html