A polytope is called k-neighborly if its (k-1)-skeleton is (combinatorially equivalent to) that of a simplex. A polytope is called cubical k-neighborly if its k-skeleton is that of a cube. Both classes of polytopes are interesting and well studied. In this talk, we are dealing with an interpolation between both classes, namely with polytopes whose k-skeleton is that of a given product of simplices. The aim is to find such 'prodsimplicial-neighborly' polytopes in small dimensions. I will explain and apply three more general methods to construct such polytopes in small dimensions and to find lower bounds on the dimension that they have to have.
This is joint work with Julian Pfeifle and Vincent Pilaud.