Choe's Hexagon and Cairo Tiling

What is the minimum perimeter for a tile on the unit square lattice? A unit square has perimeter 4, but this is not minimal. In 1989, Jaigyoung Choe determined the minimal perimeter to be [1]. In this Demonstration, the Choe irregular hexagons are shown in blue (or orange). It turns out that this tile was already well known for hexagons within an optimized Cairo tessellation.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

References
[1] J. Choe, "On the Existence and Regularity of Fundamental Domains with Least Boundary Area," Journal of Differential Geometry, 29(3), 1989 pp. 623–663. 10.4310/jdg/1214443065.
[2] J. Cepelewicz, "Mathematicians Complete Quest to Build 'Spherical Cubes'," Quanta Magazine (Feb 28, 2023). www.quantamagazine.org/mathematicians-complete-quest-to-build-spherical-cubes-20230210/#0.
[3] E. Pegg. "Choe's Irregular Hexagon" from Wolfram Community–A Wolfram Web Resource. community.wolfram.com/groups/-/m/t/2840845.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.