Quasicrystallography from Bn lattices

M. Koca, N. O. Koca, A. Al-Mukhaini, A. Al-Qanabi

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Abstract

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 B4 describes a quasicrystal structure with 8-fold symmetry. The B5 lattice leads to quasicrystals with both 5fold and 10 fold symmetries. The lattice B6 projects 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.

Original languageEnglish
Article number012016
JournalJournal of Physics: Conference Series
Volume563
Issue number1
DOIs
Publication statusPublished - Nov 26 2014

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ASJC Scopus subject areas

  • Physics and Astronomy(all)

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