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

Recent results of several authors have led to constructions of parallelotopes which are bounded remainder sets for totally irrational toral rotations. In this brief note we explain, in retrospect, how some of these results can easily be obtained from a geometric argument which was previously employe...

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Bibliographic Details
Published in:Indagationes mathematicae 2017-02, Vol.28 (1), p.138-144
Main Authors: Haynes, Alan, Kelly, Michael, Koivusalo, Henna
Format: Article
Language:English
Subjects:
Bounded remainder sets
Crystals
Cut and project sets
Deformation
Deformation mechanisms
Geometry
Lattices (mathematics)
Mathematical models
Quasicrystals
Studies
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Summary:Recent results of several authors have led to constructions of parallelotopes which are bounded remainder sets for totally irrational toral rotations. In this brief note we explain, in retrospect, how some of these results can easily be obtained from a geometric argument which was previously employed by Duneau and Oguey in the study of deformation properties of mathematical models for quasicrystals.
ISSN:0019-3577
1872-6100
DOI:10.1016/j.indag.2016.11.010