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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.
Crystallography Reports – Springer Journals
Published: Mar 1, 2008
Keywords: Crystallography and Scattering Methods
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