[math-fun] Topology of the universe

I was thinking about a simulated 3-d map of the universe, based on Hubble deep field images, and it occurred to me that a 3-d map can't really be right, based on established cosmological models. If the universe is uniform at large scales, and we are not serindipitously located near the center, then the overall topology of the universe must be some strange non-intuitive thing. What are the possible maths of such a thing?