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Affine extension of noncrystallographic Coxeter groups and quasicrystals

J. Patera·R. Twarock
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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.

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J. Patera, R. Twarock. 2002-02-16. Affine extension of noncrystallographic Coxeter groups and quasicrystals. https://doi.org/10.1088/0305-4470%2F35%2F7%2F306

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