2008/10/29 by Reinhard Lück, Dirk Frettlöh, Lück, Reinhard +1
Materials Science · Mathematics · #05A15 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Quasicrystal Structures and Properties #math.CO #math.GR #msc:05A15
paper · pdf · doi:10.48550/arxiv.0810.5299
6 pages, 4 b/w figures, 2 colour figures. Due to size/file format restrictions, the image quality is low. Better quality versions can be obtained from the second author
arxiv created 2008/10/29 · openalex publication_date 2008/10/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Colour symmetries with ten colours are presented for different tilings. In many cases, the existence of these colourings were predicted by group theoretical methods. Only in a few cases explicit constructions were known, sometimes using combination of two-colour and five-colour symmetries. Here we present explicit constructions of several of the predicted colourings for the first time, and discuss them in contrast to already known colourings with ten colours.