22nd International Conference on Integrable Systems and Quantum Symmetries | |
Quasicrystallography from Bn lattices | |
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.
【 预 览 】
Files | Size | Format | View |
---|---|---|---|
Quasicrystallography from Bn lattices | 1418KB | download |