Realizations of the associahedron and cyclohedron
Christophe Hohlweg, Carsten Lange
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 An and Bn respectively. The coordinates are obtained by an algorithm which uses an oriented Coxeter graph of type An or Bn respectively as only input and which specialises 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 fans. This settles a conjecture of N. Reading for cambrian fans of these types.
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