Geometry Workshop Obergurgl 2021

In pioneering works of Meyer and of McMullen in the early 1970s, the set of Minkowski summands of a polytope was shown to be a polyhedral cone called the type cone. Explicit computations of type cones are in general intractable. Nevertheless, we show that the type cone of the product of simplices is the cone over a simplex. This result is proved using the simple tools of Gale duality, polar duality and a result of Shephard.

This talk is based off joint work with Federico Castillo, Bennet Goeckner, Michael Ross, and Li Ying.