Geometriae Dedicata

, Volume 62, Issue 1, pp 1–17 | Cite as

Penrose tilings as coverings of congruent decagons

  • Petra Gummelt


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)

52C20 82D25 

Key words

tiling Penrose tiling aperiodic tile quasicrystal 


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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

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

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