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Recent results of several authors have led to constructions of parallelotopeswhich are bounded remainder sets for totally irrational toral rotations. Inthis brief note we explain, in retrospect, how some of these results can easilybe obtained from a geometric argument which was previously employed by Duneauand Oguey in the study of deformation properties of mathematical models forquasicrystals.

Constructing bounded remainder sets and cut-and-project sets which are bounded distance to lattices, II