Abstract
We show that the Minkowski sum of the Voronoi polytope of the root lattice and the zonotope is a 7-dimensional parallelohedron if and only if the set consists of minimal vectors of the dual lattice up to scalar multiplication, and does not contain forbidden sets. The minimal vectors of are the vectors of the classical root system . If the -norm of the roots is set equal to 2, then the scalar products of minimal vectors from the dual lattice only take the values . A set of minimal vectors is referred to as forbidden if it consists of six vectors, and the directions of some of these vectors can be changed so as to obtain a set of six vectors with all the pairwise scalar products equal to .Bibliography: 11 titles.
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