The mix of a regular polytope with a face
An abstract regular polytope is a certain kind of partially ordered set with a rank function and a flag transitive group of automorphisms. Classical examples arise from convex regular polytopes; in this case the automorphism groups are spherical Coxeter groups. Let \(P\) and \(Q\) be abstract regular polytopes with automorphism groups \(\Gamma(P)\) and \(\Gamma(Q)\), respectively. Then the mix of \(P\) and \(Q\) is a partially ordered set related to the product \(\Gamma(P)\times\Gamma(Q)\). The authors focus on the situation where \(Q\) is a face of \(P\). In particular, they prove that, for some cases, the mix of a polytope with one of its faces is again an abstract polytope. This does not hold in the general setting.
scientific article; zbMATH DE number 1887491