Кубатурные формулы на сфере, инвариантные относительно групп симметрии правильных многогранников

An algorithm of searching for the best (in a sense) cubature formulas on a sphere that are invariant under the transformations of the symmetry groups of regular polyhedrons is described. This algorithm is applied to find parameters of all the best cubature formulas of this symmetry type up to the 35th order of accuracy.