English

The second Voronoi conjecture on parallelohedra for zonotopes

Combinatorics 2013-07-30 v2 Metric Geometry

Abstract

We prove the second Voronoi conjecture on parallelohedra for zonotope. We show that for a given face-to-face tiling of d-dimensional Euclidean space into parallel copies of zonotope Z there are d vectors, connecting centers of zonotopes with common facet, that are basis of the correspondent lattice of the tiling.

Keywords

Cite

@article{arxiv.1104.0401,
  title  = {The second Voronoi conjecture on parallelohedra for zonotopes},
  author = {Alexey Garber},
  journal= {arXiv preprint arXiv:1104.0401},
  year   = {2013}
}

Comments

6 pages, available in English or Russian

R2 v1 2026-06-21T17:48:45.921Z