Orientational Sampling Schemes Based on Four Dimensional Polytopes

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