  We consider a polyhedron with zero classical resistance, i.e., a polyhedron
invisible to an observer viewing only the paths of geometrical optics rays. The
corresponding problem of scattering of plane waves by the polyhedron is
studied. The quasiclassical approximation is obtained and justified in the case
of impedance boundary conditions with a non zero absorbing part. It is shown
that the total momentum transmitted to the obstacle vanishes when the frequency
$k$ goes to infinity, and that the total cross section oscillates at high
frequencies. When the impedance $\lambda_0$ is real (i. e., there is no
absorption), it is shown that there exists a sequence of frequencies $k_n$ such
that the averages in the impedance of the total cross section over shrinking
intervals around $\lambda_0 $ go to zero as $k_n \to \infty$.
