Geodesic
The Voronoi polyhedra of the rooted lattice $E_6$ and of its dual lattice
Diskretnaya Matematika, Tome 22 (2010) no. 2, pp. 133-147

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The paper contains a detailed description of the Voronoi polyhedra $P_V(E_6)$ of the rooted lattice $E_6$ and of the lattice dual to $E_6$. For these polyhedra, tables of types of all faces and the number of faces of each type are given. It is known that the polyhedron $P_V(E_6)$ is the union of the Schläfli polyhedron $P_\mathrm{Schl}$ and its antipodal polyhedron $-P_\mathrm{Schl}$. In this paper, it is proved that is the intersection of these polyhedra. 
@article{DM_2010_22_2_a9,
     author = {V. P. Grishukhin},
     title = {The {Voronoi} polyhedra of the rooted lattice $E_6$ and of its dual lattice},
     journal = {Diskretnaya Matematika},
     pages = {133--147},
     publisher = {mathdoc},
     volume = {22},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2010_22_2_a9/}
}
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V. P. Grishukhin. The Voronoi polyhedra of the rooted lattice $E_6$ and of its dual lattice. Diskretnaya Matematika, Tome 22 (2010) no. 2, pp. 133-147. http://geodesic.mathdoc.fr/item/DM_2010_22_2_a9/