© 2003

Coverings of Discrete Quasiperiodic Sets

Theory and Applications to Quasicrystals

  • Peter Kramer
  • Zorka Papadopolos

Part of the Springer Tracts in Modern Physics book series (STMP, volume 180)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Michel Duneau, Denis Gratias
    Pages 23-62
  3. Franz Gähler, Petra Gummelt, Shelomo I. Ben-Abraham
    Pages 63-95
  4. Peter A. B. Pleasants
    Pages 185-225
  5. Rónan McGrath, Julian Ledieu, Erik J. Cox, Renee D. Diehl
    Pages 257-268
  6. Back Matter
    Pages 269-273

About this book


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.


Covering Lattice cluster clusters quasicrystals quasiperiodic quasiperiodicity tilings

Editors and affiliations

  • Peter Kramer
    • 1
  • Zorka Papadopolos
    • 1
  1. 1.Institut für Theoretische PhysikUniversität TübingenTübingenGermany

Bibliographic information