Computational determination of the largest lattice polytope diameter
Computational Geometry
2017-04-07 v1
Abstract
A lattice (d, k)-polytope is the convex hull of a set of points in dimension d whose coordinates are integers between 0 and k. Let {\delta}(d, k) be the largest diameter over all lattice (d, k)-polytopes. We develop a computational framework to determine {\delta}(d, k) for small instances. We show that {\delta}(3, 4) = 7 and {\delta}(3, 5) = 9; that is, we verify for (d, k) = (3, 4) and (3, 5) the conjecture whereby {\delta}(d, k) is at most (k + 1)d/2 and is achieved, up to translation, by a Minkowski sum of lattice vectors.
Cite
@article{arxiv.1704.01687,
title = {Computational determination of the largest lattice polytope diameter},
author = {Nathan Chadder and Antoine Deza},
journal= {arXiv preprint arXiv:1704.01687},
year = {2017}
}