Geodesic
Delaunay and Voronoi polytopes of the root lattice $E_7$ and of the dual lattice~$E_7^*$
Informatics and Automation, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Tome 275 (2011), pp. 68-86.

Voir la notice de l'article provenant de la source Math-Net.Ru

We give a detailed geometrically clear description of all faces of the Delaunay and Voronoi polytopes of the root lattice $E_7$ and the dual lattice $E_7^*$. Here three uniform polytopes related to the Coxeter–Dynkin diagram of the Lie algebra $E_7$ play a special role. These are the Gosset polytope $P_\mathrm{Gos}=3_{21}$, which is a Delaunay polytope, the contact polytope $2_{31}$ (both for the lattice $E_7$), and the Voronoi polytope $P_\mathrm V(E_7^*)=1_{32}$ of the dual lattice $E_7^*$. This paper can be considered as an illustration of the methods for studying Delaunay and Voronoi polytopes. 
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V. P. Grishukhin. Delaunay and Voronoi polytopes of the root lattice $E_7$ and of the dual lattice~$E_7^*$. Informatics and Automation, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Tome 275 (2011), pp. 68-86. http://geodesic.mathdoc.fr/item/TRSPY_2011_275_a3/

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