Geodesic
Multi-colour dynamical tilings of tori into bounded remainder sets
Izvestiya. Mathematics , Tome 79 (2015) no. 5, pp. 919-954

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We use tilings of multi-dimensional tori to construct bounded remainder sets that are finite unions of convex polyhedra. For the deviations of the distribution of points in the orbits with respect to translations of the torus over these sets, we prove a multi-dimensional version of Hecke's theorem on the distribution of fractional parts on a circle.
Keywords: multi-dimensional Hecke theorem, bounded remainder sets, polyhedra. 
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     author = {V. G. Zhuravlev},
     title = {Multi-colour dynamical tilings of tori into bounded remainder sets},
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V. G. Zhuravlev. Multi-colour dynamical tilings of tori into bounded remainder sets. Izvestiya. Mathematics , Tome 79 (2015) no. 5, pp. 919-954. http://geodesic.mathdoc.fr/item/IM2_2015_79_5_a3/