The following report concerns the application of a relaxation mesh method for the determination of the average flux within the moderator of a light water moderated, 1.027 per cent U-235, hexagonal lattice with a volume ratio (V_H2O + V_Al)/V_Uranium of 4:1. It was hoped that the calculation would enable one to determine any differences in flux which might result from the fact that the unit cell is a hexagon instead of a cylinder. Because we were primarily interested in the effect due to geometry we applied the same theory, diffusion theory, to the hexagon by means of the mesh method and to the equivalent cylinder.