#####
Séminaire Lotharingien de Combinatoire, B61Aa (2009), 13 pp.

# Nantel Bergeron, Christophe Hohlweg, Carsten Lange and
Hugh Thomas

# Isometry Classes of Generalized Associahedra

**Abstract.**
Let *W* be a finite Coxeter group. Generalized associahedra are convex
polytopes constructed from a permutahedron of *W* and an
orientation of
the Coxeter graph of *W*. They play a fundamental role in the theory
of finite type cluster algebras initiated by Fomin and Zelevinsky,
and also appear in algebraic topology. In this article, we show
that the isometries of these polytopes are given by certain
automorphisms of oriented Coxeter graphs.

Received: May 15, 2008.
Accepted: October 16, 2008.
Final Version: October 16, 2008.

The following versions are available: