On Combinatorics of Voronoi Polytopes for Perturbations of the Dual Root Lattices

Authors

Alexey Garber, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

12-2021

Abstract

The Voronoi conjecture on parallelohedra claims that for every convex polytope P that tiles Euclidean d-dimensional space with translations there exists a d-dimensional lattice such that P and the Voronoi polytope of this lattice are affinely equivalent. The Voronoi conjecture is still open for the general case but it is known that some combinatorial restrictions for the face structure of P ensure that the Voronoi conjecture holds for P. In this article, we prove that if P is the Voronoi polytope of one of the dual root lattices Dd*, E6*, E7* or E8*=E8 or their small perturbations, then every parallelohedron combinatorially equivalent to P in strong sense satisfies the Voronoi conjecture.

Comments

Original published version available at http://dx.doi.org/10.1080/10586458.2021.1994488

Recommended Citation

Garber, Alexey. 2021. “On Combinatorics of Voronoi Polytopes for Perturbations of the Dual Root Lattices.” Experimental Mathematics, December, 1–14. https://doi.org/10.1080/10586458.2021.1994488.

Publication Title

Experimental Mathematics

DOI

10.1080/10586458.2021.1994488