In topology, the Klein bottle is an example of a non-orientable surface; it is a two-dimensional manifold against which a system for determining a normal vector cannot be consistently defined. Informally, it is a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down. Other related non-orientable objects include the Möbius strip and the real projective plane. Whereas a Möbius strip is a surface with boundary, a Klein bottle has no boundary (for comparison, a sphere is an orientable surface with no boundary).
For the purposes of playing tic-tac-toe, the playing space wraps horizontally and vertically, like a torus. Unlike a torus however, the playing space is flipped in one of the directions.
In this case for example, the playing space wraps normally horizontally, but when going vertically, the space is flipped horizontally.
Support for playing on a Klein bottle, as well as other topological spaces, is coming soon to Tic-tac-toe Collection.