Affine extension of noncrystallographic Coxeter groups and quasicrystals

Abstract

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 10-fold 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.

(27 pages, to appear in J. Phys. A)

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