The Honeycomb Problem on the Sphere
Metric Geometry
2007-05-23 v1
Abstract
The honeycomb problem on the sphere asks for the perimeter-minimizing partition of the sphere into N equal areas. This article solves the problem when N=12. The unique minimizer is a tiling of 12 regular pentagons in the dodecahedral arrangement.
Cite
@article{arxiv.math/0211234,
title = {The Honeycomb Problem on the Sphere},
author = {Thomas C. Hales},
journal= {arXiv preprint arXiv:math/0211234},
year = {2007}
}