Geodesic
Polyhedral models for generalized associahedra via Coxeter elements
Journal of Algebraic Combinatorics, Tome 38 (2013) no. 1, pp. 121-158.

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Summary: Motivated by the theory of cluster algebras, F. Chapoton, S. Fomin, and A. Zelevinsky associated to each finite type root system a simple convex polytope, called generalized associahedron. They provided an explicit realization of this polytope associated with a bipartite orientation of the corresponding Dynkin diagram. In the first part of this paper, using the parametrization of cluster variables by their g-vectors explicitly computed by S.-W. Yang and A. Zelevinsky, we generalize the original construction to any orientation. In the second part we show that our construction agrees with the one given by C. Hohlweg, C. Lange, and H. Thomas in the setup of Cambrian fans developed by N. Reading and D. Speyer.
Keywords: generalized associahedra, cluster algebras, cluster complexes, g-vectors, c-sortability, cambrian fans 
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     author = {Stella, Salvatore},
     title = {Polyhedral models for generalized associahedra via {Coxeter} elements},
     journal = {Journal of Algebraic Combinatorics},
     pages = {121--158},
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     number = {1},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2013__38_1_a4/}
}
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Stella, Salvatore. Polyhedral models for generalized associahedra via Coxeter elements. Journal of Algebraic Combinatorics, Tome 38 (2013) no. 1, pp. 121-158. http://geodesic.mathdoc.fr/item/JAC_2013__38_1_a4/