On the pseudoboundary of unstable polytopes of polynomials

The pseudoboundary of a polytope is defined to be the set of all polynomials in the polytope each of which has at least one zero on the imaginary axis. It is proven that a “section” of the pseudoboundary corresponding to any frequency “ω₀” is itself a polytope whose vertices lie in the exposed two-dimensional faces of the given polytope. A simple algorithm is proposed to generate all the vertex polynomials of any section of the pseudoboundary of a polytope. An illustrative example is given