No Weak Local Rules for the 4p-Fold Tilings

作者：Bedaride Nicolas^*; Fernique Thomas

来源：Discrete & Computational Geometry, 2015, 54(4): 980-992.

DOI：10.1007/s00454-015-9740-8

• Tiling
• Quasicrystal
• Local rule
• Subshift of finite type
• Cut and projection

On the one hand, Socolar showed in 1990 that the n-fold planar tilings admit weak local rules when n is not divisible by 4 (the case corresponds to the Penrose tilings and is known since 1974). On the other hand, Burkov showed in 1988 that the eightfold tilings do not admit weak local rules, and Le showed the same for the 12-fold tilings (unpublished). We here show that this is actually the case for all the 4p-fold tilings.

• 出版日期2015-12