Abstract: 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 integral and obtained by an algorithm which uses an oriented Coxeter graph of type A or B respectively as the only input and which specializes to a procedure presented by J.-L. Loday for a certain orientation of the Coxeter graph 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. This is a joint work with Carsten Lange