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We give an explicit subword complex description of the generators of the typecone of the g-vector fan of a finite type cluster algebra with acyclic initialseed. This yields in particular a description of the Newton polytopes of theF-polynomials in terms of subword complexes as conjectured by S. Brodsky andthe third author. We then show that the cluster complex is combinatoriallyisomorphic to the totally positive part of the tropicalization of the clustervariety as conjectured by D. Speyer and L. Williams.

Minkowski decompositions for generalized associahedra of acyclic type