Our Universe?

I am at this math program and we are discussing the shape of the universe we may live in. We for the most part assume that it is basically an endless mass of space with endless length, width and height. Recently we have discussed the possibility that if we were to go far enough one way in space we would end up back where we started. It is basically like we are living in a giant 3D pac-man game. If we go out the left we show up in the right. If we go out the top we come in the bottom. If we go out the back we come in the front. That would mean if we had perfectly unobstructed vision, we could conceivable look one way and see one galaxy, and then look the other and see the exact same galaxy. If we looked the right direction, we might even see ourselves again. This concept had never even occurred to me, but why not. Maybe we have a parallel universe that isn't actually parallel, but us again. Anyway, you can stick with your understanding of the universe, or you can consider others. I mean, why not?