On Descriptions of Products of Simplices - Yu, Li; Masuda, Mikiya (Chinese annals of mathematics. Serie B, 2021)
The authors give several new criteria to judge whether a simple convex polytope in a Euclidean space is combinatorially equivalent to a product of simplices. These criteria are mixtures of combinatorial, geometrical and topological conditions that are inspired by the ideas from toric topology In addition, they give a shorter proof of a well known criterion on this subject.