## Klein bottle

The Klein bottle is a closed nonorientable surface of Euler characteristic 0, that has no inside or outside, originally described by Felix Klein. It can be constructed by gluing both pairs of opposite edges of a rectangle together giving one pair a half-twist, but can be physically realized only in four dimensions, since it must pass through itself without the presence of a hole. Its topology is equivalent to a pair of cross-caps (see Cross cap) with coinciding boundaries.

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