Finite sets of piecewise linear inequalities do not characterize zonoids

摘要

For d≥3 and every finite set Γ of piecewise linear inequalities (PLT's) the existence of a centrally symmetric convex body K is shown, which is not a zonoid although its support function fulfills all PLI's in Γ. As a corollary, itfollows that , even in IR~3, the Hlawka inequality does not characterize zonoids.