The propagation of electromagnetic waves in polyhedral domains is characterized by singularities at corners and edges. These singularities may induce a lack of density of the subspace of regular fields in the involved functional space. The aim of the talk is to give an overview of the different situations that may occur depending on the boundary condition (perfect conductor or impedance b.c.) and the material properties of the body (homogeneous or composite). We further discuss the consequences of these density or non-density results for a discretization by nodal finite elements.