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arxiv: math/0202153 · v1 · submitted 2002-02-16 · 🧮 math.GR

Affine extension of noncrystallographic Coxeter groups and quasicrystals

classification 🧮 math.GR
keywords affineconstructioncoxetergroupsnoncrystallographicpointsetscase
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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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