Klein bottle” sounds like it should be an object of some sort. But it’s not. It’s a shape. Moreover, in three dimensional space.

The closest shape to a Klein bottle would be a torus. A torus is the shape of a doughnut or O-ring. It is a hollow tube whose ends have been joined. As a result it has a separate inside and outside.

It's a surface whose top and bottom are the same (non-orientable object). So, the Mobius strip is a one-sided strip (non-orientable). The Klein bottle extends this to the next dimension, which takes the object into a fourth spatial dimension. People only observe three spatial dimensions. Projecti...