On descriptions of products of simplices

TL;DR

This paper introduces new combinatorial, geometrical, and topological criteria to determine when a convex polytope is combinatorially equivalent to a product of simplices, inspired by toric topology.

Contribution

It provides novel criteria combining combinatorial, geometrical, and topological methods for classifying polytopes as products of simplices.

Findings

New criteria for polytope classification

Criteria inspired by toric topology

Applicable to convex polytopes in Euclidean space

Abstract

We 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.