h-fold Symmetric quasicrystallography from affine Coxeter groups

摘要: One can obtain the quasicrystallographic structures from projection of higher dimensional lattices into 2D or 3D subspaces. Here we introduce a general technique applicable to any lattice described by affine Coxeter groups. It is pointed out that number h and exponents play an important role in determining principal planes onto which be projected. The quasicrystal obtained display dihedral symmetry order 2h . subspaces are determined using eigenvectors corresponding eigenvalues Cartan matrix. Examples given for 12-fold symmetric projections Coxeter-Weyl groups Wa (F4), (B6), (E6). reflection generators R1 R2 group D12 as products noted (F4) (B6) compatible with experimental data.