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arXiv · 1910.12966

Certain Hyperbolic Regular Polygonal Tiles are Isoperimetric

Jack Hirsch·Kevin Li·Jackson Petty·Christopher Xue
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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.

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Jack Hirsch, Kevin Li, Jackson Petty, Christopher Xue. 2019-11-15. Certain Hyperbolic Regular Polygonal Tiles are Isoperimetric. https://doi.org/10.1007/s10711-021-00605-2

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