KLEIN BOTTLE
Klein bottle was first described by german mathematician Felix Klein in 1882. Klein bottle is 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 mobius strip, being closed yet having no "inside" like a torus or a sphere and resulting in mobius strips if properly cut in two.