Uniquely scaled dual cells (Q2311361)

A parallelotope is a \(d\)-polytope such that one can fill facet to facet the space \(\mathbb{R}^d\) by its translation copies without gaps and intersections by inner points. The famous Voronoi conjecture states that any parallelotope is the Dirichlet-Voronoi domain of some lattice and some positive metric. The author introduces a new class of parallelotope tilings named as \(k\)-uniquely scaled tilings and proves Voronoi conjecture for the corresponding parallelotopes.