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Orientational Sampling Schemes Based on Four Dimensional Polytopes
School of Chemistry, University of Southampton, University Road, Southampton SO17 1BJ, UK
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Received: 4 February 2010; in revised form: 27 May 2010 / Accepted: 30 June 2010 / Published: 7 July 2010
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
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Cite This Article
MDPI and ACS Style
Mamone, S.; Pileio, G.; Levitt, M.H. Orientational Sampling Schemes Based on Four Dimensional Polytopes. Symmetry 2010, 2, 1423-1449.
Mamone S, Pileio G, Levitt MH. Orientational Sampling Schemes Based on Four Dimensional Polytopes. Symmetry. 2010; 2(3):1423-1449.
Mamone, Salvatore; Pileio, Giuseppe; Levitt, Malcolm H. 2010. "Orientational Sampling Schemes Based on Four Dimensional Polytopes." Symmetry 2, no. 3: 1423-1449.