I'm trying to create a "hexagonal grid" that covers the planet earth with nearly regular hexagons.
I understand that, by including 12 pentagons, the remainder of a sphere can be covered by pseudo-hexagons (a Goldberg polyhedral), but not regular hexagons.
In my application, the hexagon width will be ~1 meter (and the earth's circumference is about 40 million meters) so I'm hoping that, because my hexagon width to globe circumference ratio is so large, that I can cover the globe in nearly regular hexagons, and that the hexagon width deviation will be negligible.
Is there a function that could yield the parameters of such a Goldberg polyhedral, given a hexagon width? And is there a similar function that can tell me, for those parameters, what the standard deviation for the hexagon width is?
I'm guessing that such a function will be discrete rather than continuous. In other words, I'm guessing that there may be a finite set of values for hexagon width that have a solution.
I've read a similar question here and I understand that there is no solution that yields regular hexagons, but as I mentioned above, my application doesn't require strictly regular hexagons, so long as their irregularity is negligible.
Ideally, this function would be limited to Goldberg polyhedra that have vertices connected by a series of flat-to-flat hexagons, like this one:
