Geodesic
Exchanged toric developments and bounded remainder sets
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 26, Tome 392 (2011), pp. 95-145

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Using exchanged toric developments we construct toric tilings into bounded remainder sets. For this two methods are applied. There are a stretch of the unit cubes and a general method of multiplication of the toric developments. A multi-dimensional analogue of the Hecke theorem on the distribution of fraction parts is proved. 
@article{ZNSL_2011_392_a5,
     author = {V. G. Zhuravlev},
     title = {Exchanged toric developments and bounded remainder sets},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {95--145},
     publisher = {mathdoc},
     volume = {392},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_392_a5/}
}
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V. G. Zhuravlev. Exchanged toric developments and bounded remainder sets. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 26, Tome 392 (2011), pp. 95-145. http://geodesic.mathdoc.fr/item/ZNSL_2011_392_a5/