Realizations of the Associahedron and Cyclohedron

Abstract. We describe many different realizations with integer coordinates for the associahedron (i.e. the Stasheff polytope) and for the cyclohedron (i.e. the Bott-Taubes polytope) and compare them to the permutahedron of type A and B respectively. The coordinates are obtained by an algorithm which uses an oriented Coxeter graph of type An or Bn as only input data and which specializes to a procedure presented by J.-L. Loday for a certain orientation of An. The described realizations have cambrian fans of type A and B as normal fan. This settles a conjecture of N. Reading for cambrian lattices of these types.

• Type: Journal
• Year: 2007
• Where: DCG
• Authors: Christophe Hohlweg, Carsten E. M. C. Lange
• Keywords: DCG 2007, Different Realizations, Polytope, Stasheff Polytope