Abstract
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 quasi-classical approximation is obtained and justified in the case of impedance boundary conditions with nonzero absorbtion. It is shown that the total momentum transmitted to the obstacle vanishes as the frequency k tends 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 average of the total cross section over shrinking intervals around $\lambda_0 $ tends to zero as $k_n \to \infty$.
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