An extension of Voronoï's theorem on primitive parallelotopes (Q1345527)

The theorem of Voronoi saying that any parallelotope that is the prototile of a face-to-face primitive tiling of Euclidean space is the affine image of a Voronoi cell has been generalized by Zhitomerskii to parallelotopes all of whose belts are hexagonal. The authors extend both of these theorems by proving that each parallelotope with maximal number of facets is affinely equivalent to a unique Voronoi cell up to an orthogonal transformation.