The maximum number of complementary facets of a simplicial polytope

AbstractLet P be an (n−1)-dimensional simplicial polytype with 2n vertices labelled s1,…,sn, t1,…,tn. Call a face of P complementary if the vertices it contains all have different subscripts. We study the maximum number of complementary faces that P can have. This problem arose in the determination of the maximum possible degree of an LCP mapping. We give examples of polytopes achieving a conjectured bound, and give some results supporting the conjecture