Properties of parallelotopes equivalent to Voronoi's conjecture

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.
18 pages (submitted)

Keywords

Metric Geometry, Combinatorics

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/68059

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0307170
 http://arxiv.org/abs/math/0307170

Collections

arXiv