Affine extension of noncrystallographic Coxeter groups and quasicrystals

Unique affine extensions H aff 2 , H aff 3 and H aff 4 are determined for the noncrystallographic Coxeter groups H 2 , H 3 and H 4 . They are used for the construction of new mathematical models for quasicrystal fragments with tenfold symmetry. The case of H aff 2 corresponding to planar point sets is discussed in detail. In contrast to the cut-and-project scheme we obtain by construction finite point sets, which grow with a model specific growth parameter.