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Klein bottle
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Klein bottle A hand-blown Klein bottle, by Clifford Stoll.

Klein bottle

topology
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topology
Klein bottle
Klein bottle

Klein bottle, topological space, named for the German mathematician Felix Klein, obtained by identifying two ends of a cylindrical surface in the direction opposite that is necessary to obtain a torus. The surface is not constructible in three-dimensional Euclidean space but has interesting properties, such as being one-sided, like the Möbius strip (q.v.); being closed, yet having no “inside” like a torus or a sphere; and resulting in two Möbius strips if properly cut in two.

This article was most recently revised and updated by Amy Tikkanen.