Zonoids and Related Topics

A zonoid is a convex body in euclidean space which can be approximated, in sense of the Hausdorff metric, by finite vector sums of line segments. Several equivalent definitions are known, and zonoids appear in some surprisingly different contexts. The purpose of the present survey article is twofold. After giving some basic definitions and properties of zonotopes and zonoids, we describe the various ways in which zonoids enter the discussion of a number of seemingly unrelated topics. The stress is here on interrelations between the geometry of convex bodies and other fields. The second part treats those results and problems concerning zonoids and their generalizations which are of interest within the theory of convex bodies.

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