There have been various efforts to extend PCMs to anisotropic solvation environments without sacrificing simplicity and computational expedience. Some approaches with good formal properties, but which lack the generality that we are seeking, include methods that generalize the dielectric "constant" to a 3 × 3 tensor, as appropriate for liquid crystals, and other methods that modify the Green's function for the Coulomb potential appearing in Poisson's equation, for the case of a two-dimensional interface. However, the most convenient (and potentially general) extension is a "heterogeneous" PCM (HetPCM), in which each atomic sphere that is used to construct the solute cavity is assigned its own dielectric constant. In that way, one might hope to provide appropriate boundary conditions for a protein (for example), in which certain residues are exposed to the aqueous solvent (ε = 78) while others are buried in the protein's hydrophobic interior. For the latter environment, values ε ≈ 4 are often used in classical biomolecular electrostatics calculations, e.g., to compute pK a values. In some cases, larger values have been used for the nonpolar dielectric constant, up to ε = 10-20. The HetPCM approach has an appealing simplicity and would be easy to combine with fragment-based methods that can be used to extend the reach of quantum chemistry to proteins. To the best of our knowledge, however, this model is not derivable starting from a well-defined permittivity model ε(r), in contrast to the original (homogeneous or isotropic) PCM. Thus, HetPCM has been introduced as an ad hoc modification of the original model, which has not been rigorously tested against exact continuum electrostatics theory. We do so in the present work, using a generalized Poisson equation solver (PEqS) to provide a benchmark result for the solute-continuum polarization energy associated with any model permittivity function. This function, ε(r), is defined pointwise in three-dimensional space, allowing different spatial domains to have different permittivities. Crucial to this testing regiment is the construction of model systems for which the function ε(r) unambiguously places each continuum-exposed atomic sphere into a region where the value of ε is approximately constant, such that the model function ε(r) can be used to assign a permittivity to each atomic sphere. We accomplish this via a construction of model functions ε(r) based on Voronoi cells, that can then be mapped onto atomic dielectric constants.