Geometriae Dedicata

, Volume 62, Issue 1, pp 1–17

Penrose tilings as coverings of congruent decagons

  • Petra Gummelt

DOI: 10.1007/BF00239998

Cite this article as:
Gummelt, P. Geom Dedicata (1996) 62: 1. doi:10.1007/BF00239998


The open problem of tiling theory whether there is a single aperiodic two-dimensional prototile with corresponding matching rules, is answered for coverings instead of tilings. We introduce admissible overlaps for the regular decagon determining only nonperiodic coverings of the Euclidean plane which are equivalent to tilings by Robinson triangles. Our work is motivated by structural properties of quasicrystals.

Mathematical Subject Classifications (1991)


Key words

tilingPenrose tilingaperiodic tilequasicrystal

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Petra Gummelt
    • 1
  1. 1.Fachbereich Mathematik und InformatikErnst-Moritz-Arndt-Universität GreifswaldGreifswaldGermany