  We give the facet description of the deformation cones of graph associahedra
and nestohedra, generalizing the classical parametrization of the family of
deformed permutahedra by the cone of submodular functions. When the underlying
building set is made of intervals, this leads in particular to the construction
of kinematic nestohedra generalizing the kinematic associahedra that recently
appeared in the theory of scattering amplitudes.
