J. Ivanović (University of Belgrade), Geometrical realisations of simple polytopes obtained by truncations of nestohedra - Part 2

A family of combinatorial CW-complexes named permutoassociahedra was introduced by Kapranov and it was realised by Reiner and Ziegler as a family of convex polytopes. The polytopes in this family are "hybrids" of permutohedra and associahedra. Since permutohedra and associahedra are simple, it is natural to search for a family of simple permutoassociahedra, which is still adequate for a topological proof of Mac Lane's coherence. Such a family will be presented in this talk. Beside the combinatorial definition of the family, two different geometrical realisations also be shown. One of them, which includes Minkowski sums, delivers a general algorithm for geometrical realisations of simple polytopes obtained by truncations of nestohedra.