ABHY Associahedra and Newton polytopes of F-polynomials for cluster algebras of simply laced finite type

A new construction of the associahedron was recently given by Arkani-Hamed, Bai, He, and Yan in connection with the physics of scattering amplitudes. We show that their construction (suitably understood) can be applied to construct generalized associahedra of any simply laced Dynkin type. Unexpectedly, we also show that this same construction produces Newton polytopes for all the F-polynomials of the corresponding cluster algebras. In addition, we show that the toric variety associated to the g-vector fan has the property that its nef cone is simplicial.