Belt bodies and Helly dimension

A new class of convex bodies (called belt bodies) is introduced in this paper. Support properties of zonoids are investigated in order to introduce them. It is established that all zonoids are belt bodies; however, the class of bodies introduced is essentially broader than the class of zonoids. A complete solution of the problem of classifying belt bodies according to Helly dimension is given. Namely, a belt body has Helly dimension not exceeding $n$ if and only if it can be represented as a direct vector sum of convex sets with (topological) dimension not exceeding $n$.