Coverings of Discrete Quasiperiodic Sets: Theory and Applications to Quasicrystals

Peter Kramer · Zorka Papadopolos

iyl 2003 · Springer Tracts in Modern Physics Kitab 180 · Springer

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Coverings are efficient ways to exhaust Euclidean N-space with congruent geometric objects. Discrete quasiperiodic systems are exemplified by the atomic structure of quasicrystals. The subject of coverings of discrete quasiperiodic sets emerged in 1995. The theory of these coverings provides a new and fascinating perspective of order down to the atomic level. The authors develop concepts related to quasiperiodic coverings and describe results. Specific systems in 2 and 3 dimensions are described with many illustrations. The atomic positions in quasicrystals are analyzed.