Klein Bottle:

A Klein bottle is a 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 Moebius strip; being closed, yet having no "inside" like a torus or a sphere; and resulting in two Moebius strips if properly cut in two.

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Excerpt from the Encyclopedia Britannica without permission.