Belt diameter of -zonotopes

A Π -zonotope is a zonotope that can be obtained from permutahedron by deleting zone vectors. Any face F of codimension 2 of such zonotope generates its belt, i.e. the set of all facets parallel to F . The belt diameter of a given zonotope Z is the diameter of the graph with vertices correspondent to pairs of opposite facets and with edges connect facets in one belt. s paper we investigate belt diameters of Π -zonotopes. We prove that any d -dimensional Π -zonotope ( d ≥ 3 ) has belt diameter at most 3. Moreover if d is not greater than 6 then its belt diameter is bounded from above by 2. Also we show that these bounds are sharp. As a consequence we show that diameter of the edge graph of dual polytope for such zonotopes is not greater than 4 and 3 respectively.