  Generalized associahedra are a well-studied family of polytopes associated to
a finite-type cluster algebra and choice of starting cluster. We show that the
generalized associahedra constructed by Padrol, Palu, Pilaud, and Plamondon,
building on ideas from Arkani-Hamed, Bai, He, and Yan, can be naturally viewed
as moment polytopes for an open patch of the quotient of the cluster A-variety
with universal coefficients by its maximal natural torus action. We prove our
result by showing that the construction of Padrol, Palu, Pilaud, and Plamondon
can be understood on the basis of the way that moment polytopes behave under
symplectic reduction.
