Volume of convex hull of two bodies and related problems (Q1740479)

The author presents an useful synthesis of results, methods and open problems referring to the volume of the convex hull of two bodies having some mutual connections. The case of maximal volume polytopes inscribed in the unit sphere is discussed first in three dimensions and then in higher dimensions. The properties of volume function of the convex hull of two convex bodies are discussed and classes of pairs of convex bodies leading to special behaviour are identified. The case of simplices in three dimensional space concludes the paper. For the entire collection see [Zbl 1400.52002].