alexa Abstract | Choice of Origin, Location of Group and Uniqueness of Hermann-Mauguin Symbols
ISSN: 2320-2459

Research & Reviews: Journal of Pure and Applied Physics
Open Access

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Research Article Open Access

Abstract

It is shown that widely accepted opinion which says that Euclidean groups cannot be located in space because they are abstract groups, is incorrect. Euclidean groups are quite certain groups of operators in space and as the symmetry operations have its location di ering by fractions of the translation normal-izer of the group the group itself has also a certain location. We show, however that derivation of space groups with the use of factor systems indeed leads to groups which are not located while derivation with the use of systems of non-primitive translations leads to a set of groups di ering in location by a fraction of their Euclidean normalizer. Some examples of possible use are given.

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Author(s): Vojtech Kopsky

Keywords

Symmetry, Crystallographers, Translation normalizer, Euclidean space, Acoustics, Aerospace, Applied physics, Atomic Nuclei, Computational Physics, Fluid Mechanics, Force, Geological Research, Gravity, Industrial Physics, Internal Energy, Molecular Physics, Oscillations, Phenomenology, Pure Physics, Quantum Physics, Radiation, Statistical Physics, Thermal Properties

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