The phase diagram of nanoparticles is known to be a function of their size. Since this dependence is also a function of the surface to volume ratio and of the surface tensions, it is expected that it varies with the shape of the nanoparticles. The variation of the melting temperature of polyhedral elemental nanosolids is studied theoretically. It turns out that, in most cases, the size variation of the melting temperature of a sphere is less than for the other shapes. However, there is no general rule regarding the order of the shape parameters of the polyhedra.