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. 
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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/

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