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