Deformation Cones of Hypergraphic Polytopes

A hypergraphic polytope is a Minkowski sum of faces of the standard simplex. We study deformations of two fundamental families of hypergraphic polytopes: the graphical zonotopes and the nestohedra. Namely, we provide irredundant facet descriptions for the deformation cones of these polytopes. Moreover, we show that the faces of the standard simplex contained in the deformation cone provide a linear basis of its vector span, a result that extends to any hypergraphic polytope.