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.
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