English

Affine extension of noncrystallographic Coxeter groups and quasicrystals

Group Theory 2009-11-07 v1

Abstract

Unique affine extensions H2\affH^{\aff}_2, H3\affH^{\aff}_3 and H4\affH^{\aff}_4 are determined for the noncrystallographic Coxeter groups H2H_2, H3H_3 and H4H_4. They are used for the construction of new mathematical models for quasicrystal fragments with 10-fold symmetry. The case of H2\affH^{\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.

Keywords

Cite

@article{arxiv.math/0202153,
  title  = {Affine extension of noncrystallographic Coxeter groups and quasicrystals},
  author = {J. Patera and R. Twarock},
  journal= {arXiv preprint arXiv:math/0202153},
  year   = {2009}
}

Comments

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