Certain Hyperbolic Regular Polygonal Tiles are Isoperimetric

Published 28 Oct 2019 in math.MG | (1910.12966v2)

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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