The K4Ag18Te11, Tl4Ag18Te11, and BaHg11 cubic structures have been crystallographically analyzed within the study of the “symmetry–stability of crystalline materials” problem. The high symmetry of these structures is initiated by the local symmetry of templates, which are cuboctahedra composed of twelve Ag polyhedra around a Te anion (for the former two compounds) and twelve Hg polyhedra around a central Hg atom (for the latter compound). Similar cuboctahedra, consisting of K, Tl, and Ba cations, are formed in the second coordination sphere. The role of symmetry in the reduction of atomic degrees of freedom, which provides the structure stability, has been estimated. The qualitative stability criteria are formulated.