2001/10/31 by Michael Baake, Uwe Grimm, M. Scheffer +1 · 2 citations
Materials Science · Mathematics · Physics and Astronomy · Social Sciences · #Global Maritime and Colonial Histories #Quasicrystal Structures and Properties #cond-mat.dis-nn #cond-mat.mtrl-sci #math-ph #math.MP
paper · pdf · doi:10.1016/s0925-8388(02)00171-8
published as Journal of Alloys and Compounds 342 (2002) 195-197 · Talk presented by Max Scheffer at Quasicrystals 2001, Sendai (September 2001). 6 pages, including two colour figures
arxiv created 2001/10/31 · openalex publication_date 2002/08/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.