Certain Hyperbolic Regular Polygonal Tiles are Isoperimetric
Metric Geometry
2022-02-08 v2
Abstract
The hexagon is the least-perimeter tile in the Euclidean plane. On hyperbolic surfaces, the isoperimetric problem differs for every given area. Cox conjectured that a regular -gonal tile with 120-degree angles is isoperimetric for its area. We prove his conjecture and more.
Keywords
Cite
@article{arxiv.1910.12966,
title = {Certain Hyperbolic Regular Polygonal Tiles are Isoperimetric},
author = {Jack Hirsch and Kevin Li and Jackson Petty and Christopher Xue},
journal= {arXiv preprint arXiv:1910.12966},
year = {2022}
}
Comments
13 pages, 2 figures; added arXiv link to November paper