  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.
