Problem #WSP-4008

Problem

We start with a rectangular sheet of paper, preferably with proportions more than \(6:1\), so it looks more like a band, for now assume that one can stretch or shrink the paper band as needed. If we glue the opposite sides of the paper band in the same direction as on the picture, we will get a cylinder. What surface do we get, if we glue the circles of the cylinder in the same direction as well?