As a paradigm for the effective thermal conductivity of a densely packed dispersion of conducting filler particles in an insulating matrix, the effective conductance of a cubic array of quasi-bicones is determined analytically and its numerical properties investigated. Based upon the insights gained, the effective conductivities of simple cubic arrays of more general particles are predicted by three different approximate techniques, and the results compared with those known for simple cubic arrays of spheres. (C) 2004 Elsevier Ltd. All rights reserved.