[math-fun] Puzzle (rerun?)

I was recently reminded of this old puzzle of mine, but cannot recall if I ever posted it to math-fun. (Apologies if this is a rerun.) PUZZLE: What surface is obtained from the square [0,1]^2 by identifying each edge with the opposite edge after translating it halfway (mod 1)? (I.e., for all t in [0,1), (t,0) ~ (t + 1/2 (mod 1), 1) and (0,t) ~ (1, t + 1/2 (mod 1)). ) --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele