Cubature formulas on a sphere invariant under the dihedral group of rotations with inversion D_5d

摘要

An algorithm of searching for the best (in a sense) cubatureformulas on a sphere that are invariant under the transformations ofdihedral group of rotations with inversion D5d is described. This algorithmis applied to find the parameters of all the best cubature formulas of thissymmetry type up to the 35th order of accuracy.