For example, pairs of opposite facets of formula_6 are naturally indexed by the cocircuits of formula_21 and if we consider the oriented matroid formula_21 represented by formula_23, then we obtain a bijection between facets of formula_6 and signed cocircuits of formula_21 which extends to a poset anti-isomorphism between the face lattice of formula_6 and the covectors of formula_21 ordered by component-wise extension of formula_28. In particular, if formula_13 and formula_30 are two matrices that differ by a projective transformation then their respective zonotopes are combinatorially equivalent. The converse of the previous statement does not hold: the segment formula_31 is a zonotope and is generated by both formula_32 and by formula_33 whose corresponding matrices, formula_34 and formula_35, do not differ by a projective transformation.