In this paper we present an exact mathematical formulation for the local effective emissivities of the walls and base of a regular polyhedral cavity under the assumptions that the surfaces are diffusely reflecting, have uniform intrinsic emissivity, and are isothermal. The effective emissivities are obtained from the solution of a set of n simultaneous integral equations, each containing (n-1) integrals, where n is the number of cavity surfaces. We treat cells of the three cross-sectional shapes that can be close-packed: triangular, square, hexagonal (n=4, 5, 7 respectively, walls and base). The equations are solved using a previously-developed summation method, followed by iteration and successive substitution. The angle factors for diffuse radiant exchange are derived explicitly for each of the configurations. Singularities occur in the equations along the edge junctions. We obtain exact values for the angle factors at these singular points.
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