The Voronoi polyhedra of the rooted lattice $E_6$ and of its dual lattice

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.