Tiling properties of the zonotope formula_6 are also closely related to the oriented matroid formula_21 associated to it. First we consider the space-tiling property. The zonotope formula_6 is said to "tile" formula_39 if there is a set of vectors formula_40 such that the union of all translates formula_41 (formula_42) is formula_39 and any two translates intersect in a (possibly empty) face of each. Such a zonotope is called a "space-tiling zonotope." The following classification of space-tiling zonotopes is due to McMullen: The zonotope formula_6 generated by the vectors formula_45 tiles space if and only if the corresponding oriented matroid is regular. So the seemingly geometric condition of being a space-tiling zonotope actually depends only on the combinatorial structure of the generating vectors.