From the assumption that social structures evolve under the constraint of minimizing the total time expended on their operation, I derive equations describing the number, distribution, area, and population of territorial subdivisions. I show haw this derivation is connected with earlier ones, how an error stemming from several earlier derivations need no longer arise, and review research done to date. Many of the derived equations are new and have not yet been tested empirically. I suggest that, though the derivation is here developed for human territorial subdivisions, it should apply to territorial subdivision in other species as well.