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 $k$-gonal tile with $120$-degree angles is isoperimetric for its area. We prove his conjecture and more.

Bib(La)TeX Citation

@article{hirsch-2021-certain,
  title="Certain hyperbolic regular polygonal tiles are isoperimetric",
  author="Hirsch, Jack and Li, Kevin and Petty, Jackson and Xue, Christopher",
  journal="Geometriae Dedicata",
  volume="214",
  number="1",
  pages="65--77",
  year="2021",
  publisher="Springer"
}