  We consider the time-harmonic Maxwell system in a domain with a generalized
impedance edge-corner, namely the presence of two generalized impedance planes
that intersect at an edge. The impedance parameter can be $0, \infty$ or a
finite non-identically vanishing variable function. We establish an accurate
relationship between the vanishing order of the solutions to the Maxwell system
and the dihedral angle of the edge-corner. In particular, if the angle is
irrational, the vanishing order is infinity, i.e. strong unique continuation
holds from the edge-corner. The establishment of those new quantitative results
involve a highly intricate and subtle algebraic argument. The unique
continuation study is strongly motivated by our study of a longstanding inverse
electromagnetic scattering problem. As a significant application, we derive
several novel unique identifiability results in determining a polyhedral
obstacle as well as it surface impedance by a single far-field measurement. We
also discuss another potential and interesting application of our result in the
inverse scattering theory related to the information encoding.
