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Crystallographic point groups in five dimensions
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Michael James Downward
Published/Copyright:
November 19, 2010
Abstract
This paper describes an approach to the deduction and labeling of crystallographic point groups in n-dimensional spaces where n is an odd number. It shows that point groups in such spaces may be formed from the generators of rotational groups and a single inversion operation characteristic of the odd dimension. Results are given for 188 of the 955 crystallographic point groups in a five dimensional space and the extension to the remainder of the groups is made clear. Since 3 is an odd number, the 32 classical point groups are used to illustrate the use of generators for this purpose. Further extensions to seven dimensions and to even dimensions are then discussed.
Published Online: 2010-11-19
Published in Print: 2011-01
© by Oldenbourg Wissenschaftsverlag, Welshpool, Germany
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Keywords for this article
Five dimensional;
Point groups;
Laue sets;
Group generators;
Penta-inversion
Articles in the same Issue
- Low amplitude, low frequency elastic measurements using Dynamic Mechanical Analyzer (DMA) spectroscopy
- Nascent zeolite frameworks grown from amorphous gels – identification and prospects for crystal engineering
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- Temperature-dependent structural transformations of hydrothermally synthesized cubic Li2TiO3 studied by in-situ neutron diffraction
- Synthesis, crystal structure, electrical and thermal transport properties of the skutterudite-derivative RhGe1.5–xSe1.5+x
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- Ab-initio study of Al1–xGaxSb compound
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- Synthesis, structure and properties of Nd2BC containing the trans-dibora–(1,3)-butadiene [C=B–B=C]8–-unit
