In mathematics, the **Klein bottle** is a certain non-orientable surface, *i.e.*, a surface (a two-dimensional topological space) with no distinct “inner” and “outer” sides. Other related non-orientable objects include the Möbius strip and the real projective plane. Whereas a Möbius strip is a two dimensional object with one side and one edge, a Klein bottle is a two dimensional object with one side and *no* edges. (For comparison, a sphere is a two dimensional object with no edges and two sides.)

The Klein bottle was first described in 1882 by the German mathematician Felix Klein. It was originally named the *Kleinsche Fläche* “Klein surface”; however, this was incorrectly interpreted as *Kleinsche Flasche* “Klein bottle”, which ultimately led to the adoption of this term in the German language as well.

The Klein bottle

immersed in three-dimensional space.

~~> http://en.wikipedia.org/wiki/Klein_bottle

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