 Its surface is "flat" in the same sense that the surface of a cylinder is "flat".In 3 dimensions one can bend a flat sheet of paper into a cylinder without stretching the paper, but you cannot then bend this cylinder into a torus without stretching the paper (unless you give up some regularity and differentiability conditions, see below).A simple 4-dimensional Euclidean embedding of a rectangular flat torus (more general than the square one) is as follows