I have been looking at the following fundamental polygon: $A^{-1} B A^{-1} B$.
After thinking about it I believe this should create a torus, is this right? And if not what shape does it create?
I suspect I am wrong because this article suggests that the only fundamental polygons that create a torus are: $A B A^{-1} B^{-1}$ and a hexagonal one.
Indeed $ABA^{-1}B^{-1}$ represents the torus. As you can see in this animation.
$ABAB$ represents the projective plane. For further information visit Wikipedia. Here is a picture:
EDIT: Maybe it is not that obvious to you, but by cutting the square of the representation $A^{-1}BA^{-1}B$ along the diagonal line and by gluing things in another order, we get exactly the projective plane $ABAB$ (with the picture anove) or $C^2$ (as in the picture below).