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A closed surface with only one side, formed by passing one end of a tube through the side of the tube and joining it to the other end.

*‘Gluing the top of the Möbius band to the bottom would give you a compact Klein bottle, a complicated shape that is impossible to draw properly in three dimensions.’**‘The Klein bottle is a very precise mathematical construct.’**‘I've never summoned up enough nerve to ask Martin if he chose the house for its address or for its topology, which I suspect on close examination would prove similar to a Klein bottle.’*

1940s named after Felix Klein (1849–1925), the German mathematician who first described it.

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