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Symmetry 2010, 2(3), 1423-1449; doi:10.3390/sym2031423
Article

Orientational Sampling Schemes Based on Four Dimensional Polytopes

,
 and *
School of Chemistry, University of Southampton, University Road, Southampton SO17 1BJ, UK
* Author to whom correspondence should be addressed.
Received: 4 February 2010 / Revised: 27 May 2010 / Accepted: 30 June 2010 / Published: 7 July 2010
(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)
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Abstract

The vertices of regular four-dimensional polytopes are used to generate sets of uniformly distributed three-dimensional rotations, which are provided as tables of Euler angles. The spherical moments of these orientational sampling schemes are treated using group theory. The orientational sampling sets may be used in the numerical computation of solid-state nuclear magnetic resonance spectra, and in spherical tensor analysis procedures.
Keywords: polytope; polychora; group theory; Schl¨afli symbols; powder averaging; orientational sampling; solid-state nuclear magnetic resonance polytope; polychora; group theory; Schl¨afli symbols; powder averaging; orientational sampling; solid-state nuclear magnetic resonance
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Mamone, S.; Pileio, G.; Levitt, M.H. Orientational Sampling Schemes Based on Four Dimensional Polytopes. Symmetry 2010, 2, 1423-1449.

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