I heard that you can obtain a real projective plane by gluing a disk to a Mobius band. But then I thought: if you cut a disk out of a Klein bottle (1 face, 0 edges) you'd get a shape with 1 face and 1 edges. This sounds a lot like a mobius band, but clearly isn't because that would mean reinserting the disk would yield a Klein bottle, not the aforementioned projective plane. What do you get instead?
