  We consider the electromagnetic scattering from a convex polyhedral PEC or
PMC obstacle due to a time-harmonic incident plane wave. It is shown that the
modulus of the far-field pattern in the backscattering aperture possesses a
certain local maximum behavior. Using the local maximum indicating phenomena,
one can determine the exterior unit normal directions, as well as the face
areas, of the front faces of the obstacle. Then we propose a recovery scheme of
reconstructing the obstacle by phaseless backscattering measurements. This work
significantly extends our recent study in [12] from two dimensions and acoustic
scattering to the much more challenging three dimensions and electromagnetic
scattering.
