Penrose tilings as coverings of congruent decagons
Received: 01 July 1994 Revised: 24 March 1995 DOI:
Cite this article as: Gummelt, P. Geom Dedicata (1996) 62: 1. doi:10.1007/BF00239998 Abstract
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 References
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