The question of the shape of the universe has always fascinated me. I don't mean "shape" as how something looks like from the outside, because the universe is everything and there isn't an outside (unless you count God and the Angels). You discover the shape of the universe in the same way as you might discover the shape of a network of corridors in a large hotel: by walking all over the place until you get the hang of it. It could go on for ever (the universe, not the hotel - though some hotels do seem to be infinite) but I like to leave this to the aforesaid God. It could, for instance, be a sort of higher dimensional version of the Klein bottle (wikipedia.org/wiki/Klein_bottle).
Hmm... actually, deeper down, I know that ultimate existence is not the play-infinities of mathematics, but truly transcendent infinity.