Colour symmetry of 25 colours in quasiperiodic patterns

Abstract

Coloured periodic and quasiperiodic patterns with 25 colours and colour symmetry are described for four-, six-, eight-, ten- and twelvefold symmetries. Eightfold, twelvefold and some fourfold patterns are related to coincidence site lattices (CSLs). The procedures of delineation of coloured patterns with 25 colours must consider the property of a square number. Procedures for tenfold patterns need special consideration and allow the description of superstructures.

Keywords:

• quasicrystals
• colour symmetry
• superstructure
• coincidence site lattice

Acknowledgments

I am grateful for the collaboration during the last years with several colleagues on both colour symmetries and coincidence site lattices. Michael Baake, Uwe Grimm and Ron Lifshitz assisted in the preparation of the present manuscript. Further advice from two unknown referees and the Guest Editor, Shelomo Ben-Abraham, is appreciated.