On the volume of the convex hull of $d+1$ segments in $\mathbb{R}^d$

Abstract

Let d ≥ 2, m ≥ d, and u1, . . . , um be non-zero vectors linearly spanning R d . The note is devoted to the problem of minimizing the volume of the polytopes, where, for j = 1, . . . , m, I j is a translate of conv{o, u j }. The solution of this problem for the case m = d was previously known. For the case m = d+1 the minimal volume is evaluated and the class of minimizing polytopes P is studied.