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Affine extension of noncrystallographic Coxeter groups and quasicrystals

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Publication details

JournalJournal of Physics A: Mathematical and General
DatePublished - 22 Feb 2002
Issue number7
Number of pages24
Pages (from-to)1551-1574
Original languageEnglish


Unique affine extensions H-2(aff), H-3(aff) and H-4(aff) 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-2(aff) 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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