Кубатурные формулы на сфере, инвариантные относительно группы вращений диэдра с инверсией $\mathrm{D_{5d}}$

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