Voronoi's conjecture for extensions of Voronoi parallelohedra (Q5925156)

Let \(I\) be a segment in the \(d\)-dimensional Euclidean space \(\mathbb E^d\) and let \(P\) be a parallelohedron in \(\mathbb E^d\). Denote by \(P+I\) the Minkowski sum of \(P\) and \(I\). In this paper the author proves that Voronoi's conjecture for \(P\) holds if and only if it holds for \(P+I\). Recall that the Voronoi's conjecture states that every parallelohedron is a Voronoi parallelohedron in some Euclidean space \(\mathbb E^d\).