Remarks on 2-dimensional quasiperiodic tilings with rotational symmetries
A sequentially compact space of patches is constructed. Using this construction it is proved: Let \(S\) be a prototile set with a substitution rule \(\Phi\). If we have a prototile with a vertex of an angle \(\pi/n\), then there exists a tiling \(T_n\) with \(n\)-fold rotational symmetry, which is a periodic point of \(\widehat\Phi\). Furthermore, for an integer \(n\) with \(n= 5\) or \(6< n\), its tiling \(T_n\) is nonperiodic and has non-trivial action of a non-crystallographic Coxeter group.
scientific article; zbMATH DE number 5545480