On the Voronoi Conjecture for Combinatorially Voronoi Parallelohedra in Dimension 5
On the Voronoi Conjecture for Combinatorially Voronoi Parallelohedra in Dimension 5
In a recent paper, Garber, Gavrilyuk, and Magazinov [Discrete Comput. Geom., 53 (2015), pp. 245--260] proposed a sufficient combinatorial condition for a parallelohedron to be affinely Voronoi. We show that this condition holds for all 5-dimensional Voronoi parallelohedra. Consequently, the Voronoi conjecture in $\mathbb{R}^5$ holds if and only if every …