On edge-antipodal \(d\)-polytopes (Q1046747)

A convex \(d\)-polytope \(P\) is called edge-antipodal if any two vertices that determine an edge of \(P\) lie in different parallel supporting hyperplanes of \(P\). The authors introduce some ``program'' to investigate this type of polytopes, and they prove (among others) the following results on simple edge-antipodal polytopes: Simple edge-antipodal polytopes are antipodal in the usual sense, and there is a natural way to investigate arbitrary edge-antipodal polytopes to get a complete classification. Some nice characterizations of affine cubes are obtained, too.