Why the following space is homeomorphic to the Klein Bottle?
$$\Bbb R^2/ \Gamma,\qquad \Gamma:=<\alpha,\beta>$$ where $$\alpha=\begin{pmatrix} 1 & 0& 1/2\\ 0 & -1 & 1/2\\ 0 & 0 & 1 \end{pmatrix}, \quad \beta=\begin{pmatrix} 1 & 0& 0\\ 0 & 1 & 1/2\\ 0 & 0 & 1 \end{pmatrix}$$
Edit: This is exercise 2.3 (page 6) of Leonard S. Charlap's book: Bieberbach Groups and Flat Manifolds