I was asked to find a CW complex for the Möbius strip with one 0-cell, two 1-cells, and one 2-cell.
I can find a CW complex for a Möbius strip with more cells (two 0-cells, three 1-cells and a single 2-cell), but this doesn't help me.
I was hinted that I need to attach the 2-cell's boundary to $ab^2$ where $a$,$b$ are the 1-cells. I don't see why this gives me a Möbius strip. Is there a way of coming up with it "automatically" from the fundamental polygon of the Möbius strip i.e. $I \times I$ under the identification $(x,0)\approx (1-x,1)$? There seems to be two 0-cells (two corners) and I'm asked for a single 0-cell so I'm guessing it's unrelated.. if so then what is the way to come up with this?