ABSTRACT
This chapter shows that the polygonal areas met with in geography, for instance, river basins or market areas, must have on the average for large networks approximately six sides. There have been two basic approaches used for explaining hierarchical spatial systems. One approach is based on concepts of work and two-dimensional space filling; the other is based on various stochastic models, which can operate more or less removed from considerations of work and two-dimensional geometry though these factors can be built into the models. Walter Christaller in his theory of central places and their associated market areas, assumed that the hexagon produced an optimum partitioning of space on a featureless plain. The theory of mixed hexagonal hierarchies follows in the tradition of Christaller and C. W. Horton; that is, it is motivated by notions of space filling by a flow system which tends to accomplish the work it must do with a minimum expenditure of energy.
