[math-fun] Moebius-like torus name?

What does one call a tube looped around as if to make a torus, but connected clockwise-to-counterclockwise, as in this sewing pattern? z y>--C-->z y +---------+ x|w>--A-->x|w v|^ v|^ ||| ||| B|D B|D ||| ||| v|^ v|^ y|z<--C--<y|z +---------+ w x<--A--<w x Unless I'm fooling myself, this makes a way to wrap the sides of the board around for a game like Life or Langton's Ant, in such a way that the space is locally flat everywhere--without any local kinks or anomalies that would snarl the game rules. I have tried to think of such a thing so many times in the past and failed... Is this consistent? What's it called? --Steve