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.
This is joint work with Christophe Hohlweg.