Annals of Combinatorics 1 (1997) 297311Classification of Disordered Tilings Ludwig Balke Mathematisches Institut der Universität Bonn, Beringstr. 1, 53115
Bonn, Germany
Received May 7, 1997 AMS Subject Classification: 51M20 Abstract. A tiling T is a disordered realization of a periodic tiling P with symmetry group Γ if we can map the complement of a compact set of T onto the quotient P/Γ in such a way that this map respects the features of the tiling T and P. We show that the global type of a 2dimensional tiling T is determined by the periodic tiling P it is a disordered realization of, a conjugacy class of Γ which can be associated to T and a winding number. In some cases, we need in addition some kind of orientation. For higherdimensional tilings of spaces which are simply connected at infinity, e.g. R^{n} with n ≥ 3, the associated periodic tiling alone is sufficient. Keywords: tilings, disorderedmaterials
