1306.3316 (Mehmet Koca et al.)

12-fold Quasicrystallography from affine E6, B6, and F4    [PDF]

Mehmet Koca, Nazife O. Koca, Ramazan Koc

We introduce a general technique for the projections of the lattices described by the affine Coxeter groups and apply it to the projections of the lattices described by the affine Coxeter groups Wa(E6), Wa(B6) and Wa(F4) onto the Coxeter plane. These are the groups described by the Coxeter number h=12. The dihedral subgroup D12 of the Coxeter groups plays the crucial role in the symmetry of the projected set of points. We define two generators R1and R2 which act as reflection generators in the orthogonal planes where the product R1R2 describes the Coxeter element of the Coxeter group. The canonical projections (strip projections) of the lattices determine the nature of the quasicrystallographic structures with 12-fold symmetry as well as the crystallographic structures with 4-fold and 6-fold symmetry.

View original: http://arxiv.org/abs/1306.3316