Zonotopes whose cellular strings are all coherent

A cellular string of a polytope is sequence faces stacked on top each other in given direction. The poset strings, ordered by refinement, known to be homotopy equivalent sphere. subposet coherent strings the face lattice fiber polytope, hence homeomorphic In some special cases, every coherent. Such polytopes are said all-coherent. We give complete classification zonotopes with all-coherence property terms their oriented matroid structure. Although this case not an invariant, we prove that invariant.