Duality and minors of secondary polyhedra (Q803144)

Using Minkowski integration, we define the secondary polyhedron of a vector configuration \({\mathcal A}\) and study its behavior under the matroidal operations of duality, deletion and contraction. A main tool is the identification of the regular polyhedral subdivisions of \({\mathcal A}\) with the cells in the dual chamber complex. As an application we construct a non-regular triangulation of a cyclic polytope.