What Are You Playing Right Now, Part 2: Daggerfall

[halfeye]

You can't, really, even with hexes. It's gotta squish the hexagons somehow, possibly including other shapes like pentagons. There's only a handful of shapes that will make absolutely perfect polyhedrons - notably, those are the shapes of the D4, D6, D8, D12, and D20.

https://en.wikipedia.org/wiki/Truncated_icosahedron

That's hexes and pentagons. If we divide the hexagons and pentagons into triangles, and the triangles into smaller triangles, then we can make hexagons out of the small triangles, except at the exact centre of the pentagons, there are only 12 of those on the whole sphere. There's a bit of messing about in that the triangles in the pentagons aren't absolutely equilateral though they are quite close, but graphics cards naturally deal with that sort of thing.

On the other hand, why not go back to the d20, that's equilateral triangles all over and you can make hexes out of triangles very easily, inflate it so the points lie flat and it's almost perfect. You'd still get pentagons at the points, but still only 12 per sphere, and all the triangles are equilateral, so all the hexagons would be regular. Actually, thinking further, that must fail. The truncated icosahedron seems to work, in that the hexes still work across large triangle boundaries, but that can't be true of the untruncated version I think, a pity, it was a wonderful vision while it lasted.