Quasicrystallography from Bn lattices

22nd International Conference on Integrable Systems and Quantum Symmetries

Koca, M.^1 ; Koca, N.O.^1 ; Al-Mukhaini, A.^1 ; Al-Qanabi, A.^1

Department of Physics, College of Science, Sultan Qaboos University, PO Box 36, Al-Khoud, Muscat

123, Oman^1

关键词: Cubic lattice;    Group-theoretical analysis;    Higher-dimensional;    Hypercubic lattices;    Icosahedral quasicrystals;    Lattice points;    Quasicrystallography;    Rhombic dodecahedron;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/563/1/012016/pdf
DOI  :  10.1088/1742-6596/563/1/012016

来源: IOP

【 摘 要 】

We present a group theoretical analysis of the hypercubic lattice described by the affine Coxeter-Weyl group Wa(Bn). An h-fold symmetric quasicrystal structure follows from the hyperqubic lattice whose point group is described by the Coxeter-Weyl group W (Bn) with the Coxeter number h=2n. Higher dimensional cubic lattices are explicitly constructed for n 4,5,6 by identifying their rank-3 Coxeter subgroups and maximal dihedral subgroups. Decomposition of their Voronoi cells under the respective rank-3 subgroups W (A3), W (H2)×W (A1) and W (H3)lead to the rhombic dodecahedron, rhombic icosahedron and rhombic triacontahedron respectively. Projection of the lattice B4describes a quasicrystal structure with 8-fold symmetry. The B5lattice leads to quasicrystals with both 5fold and 10 fold symmetries. The lattice B6projects on a 12-fold symmetric quasicrystal as well as a 3D icosahedral quasicrystal depending on the choice of subspace of projections. The projected sets of lattice points are compatible with the available experimental data.