Certain Hyperbolic Regular Polygonal Tiles are Isoperimetric
arXiv:1910.12966 · doi:10.1007/s10711-021-00605-2
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.
13 pages, 2 figures; added arXiv link to November paper