2003/07/11 by Michel Deza, Deza, Michel, Viacheslav Grishukhin +1
Engineering · Materials Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Metric Geometry (math.MG) #Quasicrystal Structures and Properties #graph theory and CDMA systems #math.CO #math.MG
paper · pdf · doi:10.48550/arxiv.math/0307170
18 pages (submitted)
arxiv created 2003/07/11 · openalex publication_date 2003/07/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A parallelotope is a polytope whose translation copies fill space without gaps and intersections by interior points. Voronoi conjectured that each parallelotope is an affine image of the Dirichlet domain of a lattice, which is a Voronoi polytope. We give several properties of a parallelotope and prove that each of them is equivalent to it is an affine image of a Voronoi polytope.