The problem of determining the exact upper bound p_max of the number of faces in stereohedra, i.e., polyhedra of regular space partitions, is discussed. The theorem providing the reduction of the known bounds p_max of the Dirichlet partitions at the orbits of the general positions in the groups with mirror symmetry planes is proven. Based on this theorem, the estimates of p_max are obtained for stereohedra in these groups. The Dirichlet partitions at orbits of the general positions are considered for space groups of the class m3̄m. It is shown that for stereohedra of such partitions, p_max ≤ 226. Thus, the upper bound of the number of faces in stereohedra is reduced to 226 faces.