Hacker News Reader

Comment by gleenn | Hacker News Reader

IIRC it has to do with tiling the globe. You can't correctly tild a sphere with swuares. On a local level, it seems easier to reason about squares on a flat surface, but the Earth is round and Uber is international.

View on HN

Thanks! I'm still a bit confused because you can't tile the globe with hexagons either, if I understand correctly -- everything I can find online says you need a mix of hexagons and pentagons, and you can think of a soccer ball as an example.

Has Uber figured out a way to do it with just hexagons?

iirc it’s exactly 12 pentagons required to tile the sphere with hexagons, independent of hex-tiling size. So it’s almost fully consistent, and uber tries to put most of those pentagons in the ocean

That is correct. These are called Goldberg Polyhedra, and the most common example is a football/soccer ball.

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

Since cars don't need to cross water, maybe this isn't actually relevant. Uber aren't trying to model the planet, just the routes within the geographies they support.

h3 has the required pentagons in the ocean (dymaxion icosahedron vertices)

At least one of the pentagons is on Norway. And another one contains Beijing.

I think what GP is saying is if you zoom to the max level 15 there remain only 12 cells which come out as pentagons and all 12 of those are in the ocean (albeit sometimes very near shore). If you zoom to the global scale those 12 get inherited into ever larger parent cells which do cover large areas of the Earth though, as you found.

Reply on news.ycombinator.com