Fabrication of three-dimensional photonic crystals by the microexplosion techniques has recently been demonstrated by a number of groups. However, simple models which are currently used for characterizing the void-based photonic structures do not produce adequate results. Here, we suggest a new theoretical approach for analyzing the properties of the three-dimensional photonic crystals which allow to improve the results of the theoretical modeling of the photonic crystals created by the microexplosion method. In particular, we study the bandgap spectrum of the three-dimensional photonic crystals introducing a shell of a high-index material surrounding an air void in the face-centered-cubic lattice. This allows us to suggest an effective theoretical model which correlates very well with the properties of the microexplosion polymer photonic crystals produced experimentally. We also discuss some interesting effects observed in the fabricated photonic crystals which until now have not been understood due to the inadequacies of simple models.