A Klein bottle is "a closed surface with only one side; formed by passing one end of a tube through the side of the tube and joining it with the other end." Pictured above is a bottle opener shaped like a Klein bottle. It was made by Bathsheba Grossman, who explained:

The problem of beer That it is within a 'bottle', i.e. a boundaryless compact 2-manifold homeomorphic to the sphere. Since beer bottles are not (usually) pathological or "wild" spheres, but smooth manifolds, they separate 3-space into two non-communicating regions: inside, containing beer, and outside, containing you. This state must not remain.

A proposed solution Clearly the elegant course is to introduce a non-orientable manifold, which has one side and does not divide 3-space. When juxtaposed with the beer-bounding manifold described above, it acts to disrupt the continuity thereof, canceling the outdated paradigm of distinction between interior and exterior. This enables the desired interaction between beer and self.

Link via Nerdcore | Photo: Bathsheba Sculpture