I was looking at how a torus can be constructed by taking the unit square and identifying opposing sides and embedding this in $\mathbb{R}^3$ and how a Klein bottle is constructed in the same way but inverting the 'direction' of one of the sides. This raises the question, what object is obtained when inverting one of the horizontal edges' direction and also vertical.
When 'glueing' the first pair of edges, we obtain the mobius strip. But I'm not sure how one can 'glue' the second pair of edges, since they can be considered as one edge now.
