A Loday's realization for the cyclohedron

We describe 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 permutahedra of type A and B, respectively.

The coordinates are obtained by an algorithm which uses an oriented Coxeter graph of type A or B respectively as the only input and which specialises to a procedure presented by J.-L. Loday for a certain orientation of the Coxeter graph of A_n.

This is joint work with Carsten Lange.