A three-dimensional self-consistent photoionization code is developed in order to build more realistic models for asymmetric and/or inhomogeneous photoionized nebulae. With these models the assumption of spherical or plane-parallel symmetry can be dropped and models with various geometries can be treated. The gaseous region is divided into numerous cubic cells. The physical conditions in each cell are obtained taking into account the e†ect of the optical depth and the di†use radiation, which depend on the other cells. In order to compare to observational data, line intensities are calculated for the whole nebula, as well as for regions covered by a given slit. Isophotal maps are also obtained. A model for IC 4406, which is a typical example of bipolar planetary nebula, is presented. The model assumes a torus of dense material around the central star, as suggested by Sahai et al. Its presence is con-rmed by the model, in particular by the shape of the theoretical Ha)(N II) isophotal map. The chemical abundances required to explain the observed line intensities indicate that the chemical proper- ties of this bipolar nebula are not characteristic of type I planetaries. Subject headings: ISM: abundances E planetary nebulae: individual (IC 4406) E radiative transfer