The general methodology be hind 2D arbitrary geometry neutron transport AGENT code is the theory of R-functions, which al lows for simple modeling of complex geometries, and the method of characteristics, which solves the integral transport equation along characteristic neutron trajectories. This paper focuses on the extension of the methodology to ac count for 3D lattice geometries. Since the direct application of method of characteristics to 3D non-homogenized core con figuration may re quire a tremendous amount of memory and computing time, an alternative approximate solution based on coupling 2D method of characteristics and 1D diffusion solution is developed. The planar 2D method of characteristics and axial 1D diffusion solutions are coupled through the trans verse leak age. The use of a lower order 1D solution in the axial direction is justified by the fact that more heterogeneity in current PWR and BWR reactor cores occurs in the radial direction than in the axial one. In order to demonstrate the versatility and accuracy of the AGENT code, a 2D heterogeneous lattice problem, C5G7 is described in details. A theoretical description of the coupling methodology for 3D method of characteristics solution is followed by preliminary validation in comparison to the DeCART code.