Mathieu Dutour Sikirić

Perfect Delaunay polytopes

If the only deformation preserving a lattice Delaunay polytope are the isometries and homotheties, then it is called perfect. Such polytopes correspond to the extreme rays of a polyhedral cone, named the Erdahl cone. I created an infinite series of extreme Delaunay polytope, which generalize the classical Schafli polytope. Furthermore I introduced classical techniques of combinatorial optimization in this subject, which allowed us to find 2, 27 extreme Delaunay polytopes in dimension 7 and 8, respectively.