Affine extension of noncrystallographic Coxeter groups and quasicrystals

TY - JOUR

T1 - Affine extension of noncrystallographic Coxeter groups and quasicrystals

AU - Patera, Jiri

AU - Twarock, R

PY - 2002/2/22

Y1 - 2002/2/22

N2 - 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.

AB - 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.

KW - AMORPHOUS-SEMICONDUCTORS

U2 - 10.1088/0305-4470/35/7/306

DO - 10.1088/0305-4470/35/7/306

M3 - Article

SN - 0305-4470

VL - 35

SP - 1551

EP - 1574

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 7

ER -