Projective plane

The (real) projective plane is a nonorientable topological surface. Imagine taking a circular disk and gluing each point on the boundary to the point on the direct opposite side—that's what this shape is. Equivalently, take a Möbius strip and glue each boundary point to the point on the "opposite edge" (directly across the band). There are many ways to visualize this surface. This is the "cross cap" version.

I've also included a little stand that you can set the projective plane in so that it will stand vertically.