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I once ran into a similar problem with trying to make a regular grid with hexagons, except that I was trying to do a hex grid wrapped around a sphere.

Here's what I came up with:

https://wiki.haskell.org/IcoGrid

I treated the sphere as an icosahedron where each "side" is a triangular hex grid. At each vertex is a pentagonal cell. To get the sides to fit together nicely, I had to rotate them a little bit.

There may be a simpler way to do it, but it worked.




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