Abstract
A method is developed for the design of exactly uniform high-density vectorial distributions inside the 1/48th symmetry-irreducible trihedral angle of highest cubic symmetry. The first application led to a particular 489-vector distribution in the basic solid angle which extends, by permutations, to 23,472 uniformly-distributed vectors in the full 4π steradians. This density ( N = 489) meets a criterion of about one part in 10 5 set for the accuracy requirement of three-dimensional integration of functions in crystal lattice dynamics and in elastic wave theory. The dependence of the accuracy of numerical calculations on vector density is determined by comparison with exact integrals of certain octahedral functions. It is found to depend significantly on the three-dimensional anisotropy of the surfaces of these functions. A ten-decimal table of the direction cosines of the 489-vector distribution is supplied as an appendix.
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