I recently saw a YouTube video of a 2009 lecture by Lawrence Krauss. He says that we now know unambiguously that the universe (and I just mean the universe that we can see, back to the big bang, not the multiverse or the foam or any of that) is flat. But it seems to me that a flat universe with a boundary has a center, as far as I can tell. As usual, I can't do a great job imagining curved 3D space, but I can refer back to the nice 2D surfaces that Krauss used to demonstrate open, flat, and closed universes. The closed universe, represented by a sphere where the inhabitants are aware only of the 2D surface of the sphere, clearly has no edge and no center. But the flat universe, if it is finite (which it seems it must be), also has a center, yet I still hear people saying that there's no center. Krauss made one quick comment but never elaborated on it: he said something about the flat universe being "infinite in extent". I'm wary of this, because I don't know what "infinite in extent" could mean in a real universe, not to mention that lots of people seem to be confident that our universe has a finite size. So is there a center, or is it infinite in extent? And if infinite, what does that mean in practical terms? Can anyone help me to understand what I'm missing?