An isoperimetric problem for three-dimensional parallelohedra
Metric Geometry
2022-03-09 v4
Abstract
The aim of this note is to investigate isoperimetric-type problems for -dimensional parallelohedra; that is, for convex polyhedra whose translates tile the -dimensional Euclidean space. Our main result states that among -dimensional parallelohedra with unit volume the one with minimal mean width is the regular truncated octahedron.
Cite
@article{arxiv.2102.11621,
title = {An isoperimetric problem for three-dimensional parallelohedra},
author = {Zsolt Lángi},
journal= {arXiv preprint arXiv:2102.11621},
year = {2022}
}
Comments
Corrected a minor error in Remark 2. 11 pages, 1 figure, 1 table