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Licensed Unlicensed Requires Authentication Published by De Gruyter (O) August 26, 2010

Reducible Delaunay cell

Abstract

In terms of Selling's parameters, Sij, of a system of homogeneous axes, if every Sij is negative, the conditions for the three shortest among them to define the reduced cell are expressed by: |s12| ⩽ |S13 + S14|, |s21| ⩽ |S23 + S24|, |S32| ⩽ |S31 + S34|, |S23| ⩽ |S21 + S24|, |S31| ⩽ |S32 + S34|, |S13| ⩽ |S12 + S14|. Upon application of these conditions to the final result, Vf, of a series of Delaunay's transformations, it is possible to judge whether Vf contains a reduced cell or not, and if it does not, Vf can still be transformed into a reduced cell by a single step of a specific transformation. In Delaunay's procedure, ambiguities always arise whenever one or more than one zero occurs in Vf, but they can be evaded by applying the above conditions and, if necessary, by one more step of Delaunay's transformations.

Published Online: 2010-08-26
Published in Print: 1968
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