Discrete & Computational Geometry

, Volume 37, Issue 4, pp 517–543 | Cite as

Realizations of the Associahedron and Cyclohedron

Article

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 with 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 the 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 fans. This settles a conjecture of N. Reading for cambrian lattices of these types.

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Copyright information

© Springer 2007

Authors and Affiliations

  1. 1.The Fields Institute, 222 College StreetToronto, Ontario, M5T 3J1Canada
  2. 2.Fachbereich fur Mathematik und Informatik, Freie Universitat Berlin, Arnimallee 3D-14195 BerlinGermany

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