  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 remarkably simple result derives from insights about
rainbow point configurations and the work of McMullen.
