A continuous band with one twist in it. Between any two points on it, a continuous curve can be drawn on the surface demonstrating that the band is one-sided and likewise has only one edge. Formally, the Möbius band is non-orientable. The Möbius band was independently discovered by Möbius and Johann Listing in 1858.
http://www.popmath.org.uk/sculpmath/pagesm/mb.html The Möbius band in art.