In the study of Riemann surfaces, we can get lots of cool examples by identifying parallel sides of polygons. For example, by identifying the parallel sides of a square we obtain a torus. This is easy enough to imagine. However, take this figure, for example,
and identify the sides with the same color. (Ignore the dashed lines.) This is also a Riemann surface. But one that I cannot imagine. I would love to get some geometric intuition by understanding this surface.
Particularly, I am doing a project in which this surface appears very frequently. If I could draw a pretty image of this surface, it would make an awesome cover of the report. I would appreciate any hint about how I could do it.