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.

中文翻译：

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某些双曲正则多边形块是等参的

六边形是欧几里得平面中最小周长的图块。在双曲表面上，对于每个给定区域，等渗问题都是不同的。考克斯推测，具有120度角的规则k角形图块是等面积的。我们证明他的猜想等等。