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Invariants of the crystallographic system E 8 , algebraic polytopes, and 3D ordered structures

Invariants of the crystallographic system E 8 , algebraic polytopes, and 3D ordered structures Abstract It is shown that constructions of algebraic geometry select peculiar subsystems of vectors of the first coordination sphere of the 8D crystallographic lattice E 8. A correspondence between such subsystems and pairs of 4D systems of vectors specifying vertices of “algebraic” polytopes on a 3D sphere is established. A 136-vertex algebraic polytope, whose symmetry determines the structure of a number of ordered diamond-like structures, is considered as an example. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Crystallography Reports Springer Journals

Invariants of the crystallographic system E 8 , algebraic polytopes, and 3D ordered structures

Crystallography Reports , Volume 53 (2): 4 – Mar 1, 2008

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References (10)

Publisher
Springer Journals
Copyright
2008 Pleiades Publishing, Ltd.
ISSN
1063-7745
eISSN
1562-689X
DOI
10.1134/s1063774508020016
Publisher site
See Article on Publisher Site

Abstract

Abstract It is shown that constructions of algebraic geometry select peculiar subsystems of vectors of the first coordination sphere of the 8D crystallographic lattice E 8. A correspondence between such subsystems and pairs of 4D systems of vectors specifying vertices of “algebraic” polytopes on a 3D sphere is established. A 136-vertex algebraic polytope, whose symmetry determines the structure of a number of ordered diamond-like structures, is considered as an example.

Journal

Crystallography ReportsSpringer Journals

Published: Mar 1, 2008

Keywords: Crystallography and Scattering Methods

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