Projex

Projex (Projective Hex) is a Hex-like abstract strategy game: two players take turns to occupy hexagonal cells, competing to build a chain of occupied cells across the board.

For Projex, the hex grid wraps around at the edges to form a projective plane. Six pentagons (or three squares) must be included among the hexagons for the whole plane to be tiled.

A winning chain is any loop which encircles the projective plane, in the sense that it is not topologically equivalent to a trivial loop. As with Hex and Y, the game has the mathematically appealing property that when the board is full, exactly one player will have a winning chain.

References
Designer's post to sci.math describing the game
Description at gamerz.net