Delaunay polytopes of Niemeier lattices

The Delaunay polytopes of the Leech lattice is an information that has been used for a great many purposes. Here we enumerate the Delaunay polytopes for 14 Niemeier lattices out of 23. That allows us to compute the Covering radius of those lattices. More information can be available on: Adel Alahmadi, Michel Deza, Mathieu Dutour Sikirić, Patrick Solé, Covering aspects of the Niemeier lattices, European Journal of Combinatorics 80 (2019) 102--106