A factorial faceted, factorial extreme point polytope crafted from the assignment polytope

Abstract

Polytope Cⁿ is defined as the convex hull of the set of extrema of the assignment polytope less one extreme point and the facet count is then proven to be factorial. This result is interesting since it emphasizes an abrupt behavioural change - from polynomial to factorial. The loss of a single extremum 'causes' the assignment polytope to wildly 'heal' itself.