Colourings of planar quasicrystals

Details Colourings of planar quasicrystals Colourings of planar quasicrystals

2001-10-31

arxiv.org/abs/cond-mat/0110654v1

Journal of Alloys and Compounds 342 (2002) 195-197

Physics

Condensed Matter

Disordered Systems and Neural Networks

Talk presented by Max Scheffer at Quasicrystals 2001, Sendai (September 2001). 6 pages, including two colour figures

Scientific paper

10.1016/S0925-8388(02)00171-8

The investigation of colour symmetries for periodic and aperiodic systems consists of two steps. The first concerns the computation of the possible numbers of colours and is mainly combinatorial in nature. The second is algebraic and determines the actual colour symmetry groups. Continuing previous work, we present the results of the combinatorial part for planar patterns with n-fold symmetry, where n=7,9,15,16,20,24. This completes the cases with values of n such that Euler's totient function of n is less than or equal to eight.

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