Abstract

In this paper, an algorithm of search for the best (in a sense) cubature formulas on a sphere that are invariant with respect to the icosahedral group of rotations with inversion is described. This algorithm is used to find the parameters of all best cubature formulas of this symmetry type up to the 79th degree of exactness. Some parameters of the new cubature formulas of the 21st, 25th, and 29th orders of exactness are given to 16 significant digits.

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