A two-dimensional representation of a Klein bottle--a shape with no inside or outside, just one continuous surface. A true Klein bottle needs at least four dimensions; in other words, it can't be blown from glass. Two- and three-dimensional representations like this one exist to help us visualize the topology, but they are not completely faithful to the original shape. The surface cannot be built in two- or three-dimensional space without self-intersection, as shown here with the "handle" passing through the side of the surface.
Credit: Thomas Banchoff, Brown University, and Davide Cervone, Union College.