Discrete & Computational Geometry

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

Realizations of the Associahedron and Cyclohedron

  • Christophe HohlwegEmail author
  • Carsten E.M.C. LangeEmail author


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.


Convex Hull Half Space Coxeter Group Weak Order Coxeter Graph 
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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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