  It is proved that a convex polyhedral scatterer of impedance type can be
uniquely determined by the electric far-field pattern of a non-vanishing
incident field. The incoming wave is allowed to bean electromagnetic plane
wave, a vector Herglotz wave function or a point source wave incited by some
magnetic dipole. Our proof relies on the reflection principle for Maxwell's
equations with the impedance (or Leontovich) boundary condition enforcing on a
hyper-plane. We prove that it is impossible to analytically extend the total
field across any vertex of the scatterer. This leads to a data-driven inversion
scheme for imaging an arbitrary convex polyhedron.
