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. 
@article{TRSPY_2011_275_a3,
     author = {V. P. Grishukhin},
     title = {Delaunay and {Voronoi} polytopes of the root lattice $E_7$ and of the dual lattice~$E_7^*$},
     journal = {Informatics and Automation},
     pages = {68--86},
     publisher = {mathdoc},
     volume = {275},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2011_275_a3/}
}
TY  - JOUR
AU  - V. P. Grishukhin
TI  - Delaunay and Voronoi polytopes of the root lattice $E_7$ and of the dual lattice~$E_7^*$
JO  - Informatics and Automation
PY  - 2011
SP  - 68
EP  - 86
VL  - 275
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2011_275_a3/
LA  - ru
ID  - TRSPY_2011_275_a3
ER  - 
%0 Journal Article
%A V. P. Grishukhin
%T Delaunay and Voronoi polytopes of the root lattice $E_7$ and of the dual lattice~$E_7^*$
%J Informatics and Automation
%D 2011
%P 68-86
%V 275
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2011_275_a3/
%G ru
%F TRSPY_2011_275_a3
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/