Is there a general study of the symmetries of tilings in surfaces? Conway, Goodman-Strauss & Burgiel classified them on $\mathbb S^2, \mathbb R^2$ and $\mathbb H^2$, with their 'Magic Theorem'. But I found nothing about general surfaces, except for the cilinder which is an easy consequence from the result above.

I thought W. Thurston could have some results about this, but I found nothing.