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- Title
B<sub>7</sub> as a supergroup of crystal and quasicrystal symmetries.
- Authors
Stróż, Kazimierz
- Abstract
In sharp contrast to the generation of a finite group that includes all the 14 types of Bravais lattices as its subgroups [Hosoya (2000). Acta Cryst. A 56, 259-263; Hosoya (2002). Acta Cryst. A 58, 208], it was proved that a signed permutation group Bk may be interpreted as the supergroup of both crystal and quasicrystal symmetries. Minimal dimension k = 6 is adequate for lattices referred to their three non-coplanar shortest vectors, or for symmetry groups of most quasicrystal types. If one prefers complete, well defined semi-reduced lattice descriptions or needs a dodecagonal group, the B7 supergroup is necessary. All considered matrix groups correspond to isometric transformations in extended k-bases and may be easily derived from B7 and projected onto three-dimensional crystallographic space. Three models of extended bases are proposed: semi-reduced, cyclic and axial. In all cases additional basis vectors are strictly (functionally) related to three original basis vectors.
- Subjects
CRYSTALS; QUASICRYSTALS; SYMMETRIES (Quantum mechanics)
- Publication
Acta Crystallographica. Section A, Foundations & Advances, 2017, Vol 73, Issue 2, p135
- ISSN
2053-2733
- Publication type
Article
- DOI
10.1107/S2053273316019586