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by mtrovo 2532 days ago
They go into some detail on this talk https://youtu.be/ay2uwtRO3QE?t=712.

What I get from their explanation is that hexagon is a better shape for map grids because they are the most complex shape that can tesselate (the other two are triangles and squares). As they are more close to a circle, distances within a cell are more stable, also computing the distance from a cell center to its neighbours is stable in hexagons as well.

I think the reason hex is not more common is that subdivisions are hard to create compared to triangles or squares. Uber solved this by subdividing in 7 smaller hex and tilting it so they cover the bigger shape with some small overlap.

Also a big problem is distortion, I never thought this would be that huge of a problem but it makes sense. They go into a lot of the details later on the same video.

3 comments

Which is why, btw, Hexagons have been used for decades in wargames (and - to a more limited extent, in other types of boardgames).
> hexagon is a better shape for map grids because they are the most complex shape that can tesselate

[Penrose tiling intensifies]

I think it's clear what they meant was not actually 'the most complex shape' but the regular polygon with the most sides that can tessellate.
Autocomplete of 'most compact'.
The Techzing podcast talked about the origin of this several years ago, back when one of the hosts had a critical role in its creation. Good stuff.