Isotropic conductivity of two-dimensional three-component symmetric composites

The effective DC conductivity problem of isotropic, two-dimensional (2D), t hree-component, symmetric, regular composites is considered. A simple cubic equation with one free parameter for sigma (e)(sigma (1), sigma (2), sigma (3)) is suggested whose solutions automatically have all the exactly known properties of that function. Numerical calculations on four different symm etric, isotropic, 2D, three-component, regular structures show a non-univer sal behaviour of sigma (e)(sigma (1), sigma (2), sigma (3)) with an essenti al dependence on micro-structural details, in contrast with the analogous t wo-component problem. The applicability of the cubic equation to these stru ctures is discussed. An extension of that equation to the description of ot her types of 2D three-component structures is suggested, including the case of random structures.