Construction of cubature formulas on a sphere consistent with a regular hexagonal lattice

In the problems of radiation and neutron transport it is required to calculate the angular moments of the particle distribution function. Optimized cubature formulas for calculating integrals over the sphere of angular directions in the centers of faces and in the center of a regular hexagonal prism are constructed. The constructed formulas can be used in the development of programs for the numerical solution of the particle transport equation by the Carlson method and the long characteristics method. The optimal ratio of the characteristic linear dimensions of the prismatic cell to achieve the minimum error of cubature formulas is found.