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Orientational sampling schemes based on four dimensional polytopes

Orientational sampling schemes based on four dimensional polytopes
Orientational sampling schemes based on four dimensional polytopes
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.
polytope, polychora, group theory, schl¨afli symbols, powder averaging, orientational sampling, solid-state nuclear magnetic resonance
1423-1449
Mamone, Salvatore
b4a7783d-af9c-482a-afde-a77a06460b4b
Pileio, Giuseppe
13f78e66-0707-4438-b9c9-6dbd3eb7d4e8
Levitt, Malcolm H.
bcc5a80a-e5c5-4e0e-9a9a-249d036747c3
Mamone, Salvatore
b4a7783d-af9c-482a-afde-a77a06460b4b
Pileio, Giuseppe
13f78e66-0707-4438-b9c9-6dbd3eb7d4e8
Levitt, Malcolm H.
bcc5a80a-e5c5-4e0e-9a9a-249d036747c3

Mamone, Salvatore, Pileio, Giuseppe and Levitt, Malcolm H. (2010) Orientational sampling schemes based on four dimensional polytopes. Symmetry, 2 (3), 1423-1449. (doi:10.3390/sym2031423).

Record type: Article

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.

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More information

Published date: 7 July 2010
Keywords: polytope, polychora, group theory, schl¨afli symbols, powder averaging, orientational sampling, solid-state nuclear magnetic resonance

Identifiers

Local EPrints ID: 178383
URI: http://eprints.soton.ac.uk/id/eprint/178383
PURE UUID: f4cfe9ab-7dc5-4be9-a383-fbffd9b28f29
ORCID for Giuseppe Pileio: ORCID iD orcid.org/0000-0001-9223-3896
ORCID for Malcolm H. Levitt: ORCID iD orcid.org/0000-0001-9878-1180

Catalogue record

Date deposited: 24 Mar 2011 13:55
Last modified: 07 Oct 2020 07:38

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