Affine extension of noncrystallographic Coxeter groups and quasicrystals
J. Patera, R. Twarock
Abstract
Unique affine extensions H2, H3 and H4 are determined for the noncrystallographic Coxeter groups H2, H3 and H4. They are used for the construction of new mathematical models for quasicrystal fragments with 10-fold symmetry. The case of H2 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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