A note on the dual description of projected polytopes

The inequalities which describe the projection Q of a given polytope P onto a subspace are usually generated by an elimination procedure of Fourier–Mozkin type. In this note we give a dual approach for the description of Q. In fact, the vertices of a dual polytope serve as indices for the describing inequalities. Moreover we show how the redundancy of inequalities is connected with the existence of Slater points in the images of a set-valued mapping.