The Curvature of the Universe Determines the Shapes

The curvature of the universe determines what shapes are possible. If space is flat, then it can't be a sphere or close straght. You have to build a universe where every piece of space has that curvature and so have it all fit together without any edges. There are only a few shapes that are possible. But if we measure space to be flat, then there's no shape. It can't be an infinite flat universe. We could also consider more exotic shapes, like a doughnut with two holes in it. I don't even know what you call that - double bagle?