jr recently spammed me with a very interesting article, see:

https://www.quantamagazine.org/mathematicians-complete-quest-to-build-spherical-cubes-20230210

Therein, the authors reference J. Choe's tiling of a 2D plane with a hexagon
with minimal perimeter.

The original paper has a diagram with angles,

http://newton.kias.re.kr/~choe/fundamental.pdf

and another paper has the lengths of the sides.

https://www.researchgate.net/publication/267246574_Spherical_Cubes_Optimal_Foams_from_Computational_Hardness_Amplificat
ion

From that data, I was able to do a few rotations and use symmetry to getthe rest
of the points, and make a prism, which tiles the plane very nicely.

Next task is going to figure out how to make this into a pigment {function{}}
pattern, and color it like the inbuilt hexagon pattern.

Post a reply to this message

Attachments:
Download 'choehexagon.png' (90 KB)

Preview of image 'choehexagon.png'