A method is presented to compute the electron-optical phase shift for a magnetized polyhedral nanoparticle, with either a uniform magnetization or a closure domain . The method relies on an analytical expression for the shape amplitude, combined with a reciprocal-space description of the magnetic vector potential. The model is used to construct two building blocks from which more complex structures can be generated. Phase computations are also presented for the five Platonic and 13 Archimedean solids. Fresnel and Foucault imaging mode (...) simulations are presented for a range of particle shapes and microscope imaging conditions. (shrink)