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Crystallographic and Quasicrystallographic Lattices from the Finite Groups of Quaternions

R. Bruce King ; Department of Chemistry, University of Georgia, Athens, Georgia 30602, USA

Puni tekst: engleski, pdf (3 MB) str. 805-812 preuzimanja: 233* citiraj
APA 6th Edition
King, R.B. (1996). Crystallographic and Quasicrystallographic Lattices from the Finite Groups of Quaternions. Croatica Chemica Acta, 69 (3), 805-812. Preuzeto s https://hrcak.srce.hr/177112
MLA 8th Edition
King, R. Bruce. "Crystallographic and Quasicrystallographic Lattices from the Finite Groups of Quaternions." Croatica Chemica Acta, vol. 69, br. 3, 1996, str. 805-812. https://hrcak.srce.hr/177112. Citirano 21.06.2021.
Chicago 17th Edition
King, R. Bruce. "Crystallographic and Quasicrystallographic Lattices from the Finite Groups of Quaternions." Croatica Chemica Acta 69, br. 3 (1996): 805-812. https://hrcak.srce.hr/177112
Harvard
King, R.B. (1996). 'Crystallographic and Quasicrystallographic Lattices from the Finite Groups of Quaternions', Croatica Chemica Acta, 69(3), str. 805-812. Preuzeto s: https://hrcak.srce.hr/177112 (Datum pristupa: 21.06.2021.)
Vancouver
King RB. Crystallographic and Quasicrystallographic Lattices from the Finite Groups of Quaternions. Croatica Chemica Acta [Internet]. 1996 [pristupljeno 21.06.2021.];69(3):805-812. Dostupno na: https://hrcak.srce.hr/177112
IEEE
R.B. King, "Crystallographic and Quasicrystallographic Lattices from the Finite Groups of Quaternions", Croatica Chemica Acta, vol.69, br. 3, str. 805-812, 1996. [Online]. Dostupno na: https://hrcak.srce.hr/177112. [Citirano: 21.06.2021.]

Sažetak
Quaternions are ordered quadruples of four numbers subject to
specified rules of addition and multiplication, which can represent
points in four-dimensional (4D) space and which form finite groups
under multiplication isomorphic to polyhedral groups. Projection of
the 8 quaternions of the dihedral group D2h, with only two-fold
symmetry, into 3D space provides a basis for crystal lattices up to
orthorhombic symmetry (a "* b "* c). Addition of three-fold symmetry
to D2h gives the tetrahedral group Td with 24 quaternions, whose
projection into 3D space provides a basis for more symmetrical
crystal lattices including the cubic lattice (a = b = c). Addition of
five fold symmetry to Td gives the icosahedral group Ih with 120
quaternions, whose projection into 3D space introduces the --J5 irrationality and thus cannot provide the basis for a 3D crystal lattice.
However, this projection of Ih can provide a basis for a 6D lattice
which can be divided into two orthogonal 3D subspaces, one
representing rational coordinates and the other representing COOI'-
dinates containing the --J5 irrationality similar to some standard
models for icosahedral quasicrystals.

Hrčak ID: 177112

URI
https://hrcak.srce.hr/177112

Posjeta: 323 *