Das Volumen spezieller konvexer Polytope. (On the volume of special convex polytopes) (Q1114935)

The following problem was posed by E. Heil in 1974: Let Q be the convex hull of n line segments in \({\mathbb{R}}^ n\). Is the volume of Q not smaller than the volume of S, where S is an n-simplex defined by translates of these n line segments with one common endpoint? A positive answer to a natural generalization of this question was given by \textit{P. McMullen} with characterizations of the equality case [Math. Proc. Camb. Philos. Soc. 91, 91-97 (1982; Zbl 0481.52003)]. The present paper contains an elementary proof of the restrictions of McMullen's results to Heil's original formulation of the problem, given above.