Type cones and products of simplices

A polytope $P$ is the convex hull of finitely many points in Euclidean space. For polytopes $P$ and $Q$, we say that $Q$ is a Minkowski summand of $P$ if there exists some polytope $R$ such that $Q+R=P$. The type cone of $P$ encodes all of the (weak) Minkowski summands of P. In general, combinatorially isomorphic polytopes can have non-isomorphic type cones. We will first consider type cones of polygons, and then show that if $P$ is combinatorially isomorphic to a product of simplices, then the type cone is simplicial. This is joint work with Federico Castillo, Joseph Doolittle, Michael Ross, and Li Ying.