Discrete & Computational Geometry

, Volume 8, Issue 1, pp 1–25

Aperiodic tiles

  • Robert Ammann
  • Branko Grünbaum
  • G. C. Shephard

DOI: 10.1007/BF02293033

Cite this article as:
Ammann, R., Grünbaum, B. & Shephard, G.C. Discrete Comput Geom (1992) 8: 1. doi:10.1007/BF02293033


A set of tiles (closed topological disks) is calledaperiodic if there exist tilings of the plane by tiles congruent to those in the set, but no such tiling has any translational symmetry. Several aperiodic sets have been discussed in the literature. We consider a number of aperiodic sets which were briefly described in the recent bookTilings and Patterns, but for which no proofs of their aperiodic character were given. These proofs are presented here in detail, using a technique with goes back to R. M. Robinson and Roger Penrose.

Copyright information

© Springer-Verlag New York Inc. 1992

Authors and Affiliations

  • Robert Ammann
    • 1
  • Branko Grünbaum
    • 2
  • G. C. Shephard
    • 3
  1. 1.P.O. Box 265BillericaUSA
  2. 2.University of Washington GN-50SeattleUSA
  3. 3.University of East AngliaNorwichEngland