5 in line game, on Klein bottle

First, you have to make Klein bottle. Do not bother to use time as the fourth dimension. Just take a piece of paper, draw a game board, 48 cells, 6 by 8, and then glue the edges. The two longer edges are glued together in the same direction; the two shorter edges are glued together in the opposite direction. You can easily do it in your imagination, of course, because imagination is infinite-dimensional. You could even imagine the board itself, but that's harder.

Now you can play Five In Line on the board.