The heat transfer characteristics for an insulated regular polyhedron (or sphere) are investigated by using a regular polygon top solid wedge thermal resistance (RPSWT) model as well as the interior area thermal resistance model R-th = t/K-s/[(1 - alpha)A(2) + alphaA(3)] with a surface area weighting factor alpha. The errors of the results generated by an interior area thermal resistance model can be obtained by comparing the exact results generated by an RPSWT model. The accurate solution can be obtained without error at the optimum alpha(opt) with their relative t/R-2. The relation between alpha(opt) and t/R-2 is alpha(opt) = 1/(2 + t/R-2). The value of alpha(opt) is between 0-0.5 and is independent of container size R-2/R-cr but strongly dependent on the insulated thickness t/R-2 (for example, t/R-2 = 0.5, alpha(opt) = 0.4). The interior area thermal resistance model with the optimum value alpha(opt) should also be applied to an insulated container with arbitrary shape within a small amount of error. The parameter R-2 can be evaluated by measuring the container surface area A2 and letting A(2) = 4piR(2)(2). It is also found that the conventional constant surface area plate model is not suitable to be used to analyze insulated polyhedra. There exists quite a large error even in situations with large container size with medium insulation thickness. (C) 2003 Elsevier Ltd. All rights reserved.