Voronoi's Conjecture for extensions of Voronoi parallelohedra

Alexander Magazinov

Let $I$ be a segment in the $d$-dimensional Euclidean space ${\mathbb{E}}^d$. Let $P$ and $P+I$ be parallelohedra in ${\mathbb{E}}^d$, where "+" denotes the Minkowski sum. We prove that…