# Question on Conway tilings

Conway in http://olympiads.mccme.ru/lktg/2009/4/articles/conway.pdf provided some elegant techniques for identifying tiling of simply connected regions. Are there similar techniques for regions that are not simply connected such as torus in higher dimensions (in the sense that the tiles can be conformal shaped based on their position on the torus)?

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Is there a positive result for tiling on $2$-dimensional surface of torus in $\Bbb R^3$? Is there a reference for negative result? –  J.A Oct 28 '13 at 7:15