Geodesic
Dividing toric tilings and bounded remainder sets
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 30, Tome 440 (2015), pp. 99-122

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An infinite sequence of dividing two-dimensional toric tilings is constructed by using differentiation of toric developments admitting a rearrangement. We prove that the nucleus of these tilings is a bounded remainder set. 
@article{ZNSL_2015_440_a7,
     author = {V. G. Zhuravlev},
     title = {Dividing toric tilings and bounded remainder sets},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {99--122},
     publisher = {mathdoc},
     volume = {440},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_440_a7/}
}
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V. G. Zhuravlev. Dividing toric tilings and bounded remainder sets. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 30, Tome 440 (2015), pp. 99-122. http://geodesic.mathdoc.fr/item/ZNSL_2015_440_a7/