  It has been established in recent years how to approach acyclic cluster
algebras of finite type using subword complexes. In this paper, we continue
this study by describing the c- and g-vectors, and by providing a conjectured
description of the Newton polytopes of the F-polynomials. In particular, we
show that this conjectured description would imply that finite type cluster
complexes are realized by the duals of the Minkowski sums of the Newton
polytopes of either the F-polynomials, or of the cluster variables,
respectively.
