This paper gives a theoretical basis for calculating Fraunhofer diffraction patterns of arbitrary polyhedron particles. It is shown that this solution can be used for calculating a scatter matrix adapted to the particle shape in a straightforward manner. Some simulations were made to show the difference between the size distribution by volume obtained with a scatter matrix for spheres and with that for the appropriate shape. Finally, some experimentally measured signatures from platelets and rods are evaluated in order to show that the spherical equivalent diameter could be accurately retrieved.