ABSTRACT
A subset S of is called antipodal if for every pair of points x,yЄS, one can find a linear function l on such that
It is known that an antipodal set in has at most 2n elements. In particular, its convex hull is a polytope. The definition implies that an antipodal set coincides with the vertex set of its convex hull. We shall call a convex polytope P antipodal if its vertex set is antipodal. Thus, there is a one-to-one correspondence between antipodal sets and antipodal polytopes. For reference and related results see [3], [6], [7].
