The simple cubic lattice model of cubic particles A dispersed in a continuous (polymeric) matrix B (and occupying a volume fraction 0 <= V-A <= 1 therein), introduced in Parts I and II to establish the meaningful applicability of the Maxwell and Wiener equations to binary composite-medium permeability properties up to V-A -> 1, is here applied to modeling the practically important case of a three-phase composite medium, where the third phase is considered to take the (idealized) form of zones surrounding particles A which exhibit permeability properties differing substantially from those of the bulk matrix It is shown, both theoretically and by application to various existing experimental data, that replacing the spherical particles, commonly assumed in such modeling, with cubic ones, leads to remarkable gains in model simplicity and internal consistency, in practical applicability, and ultimately in physical understanding of the observed variety of 3-phase composite-medium permeability behavior. (C) 2015 Elsevier Ltd. All rights reserved