[adolgert]

Dumb question: I've put points on a sphere using a Fibonacci series, then relaxed them and triangulated them, and there are some 5's and 7's, not all hexagons. I thought an all-hexagon tiling wasn't possible. How do they do it?

[ravar]

There are 12 pentagons conveniently placed over water. The docs are a pretty interesting read. https://eng.uber.com/h3/

[progbits]

That is a clever solution! For a transportation company at least.

I wonder what happens if an artificial island and a major city pops up in one of those pentagons - presumably a fun tech debt to tackle :)

[robinhouston]

There’s a 2018 blog post from Uber Engineering[0] which has more technical details about the system, and explains:

> Since it is not possible to tile the icosahedron with only hexagons, we chose to introduce twelve pentagons, one at each of the icosahedron vertices.

0. https://eng.uber.com/h3/

[bloopernova]

They distort the hexagons as you go further north.

https://observablehq.com/@four43/h3-index-visualizer

https://imgur.com/a/SgDfJkG is an example

[ritwikgupta]

The warping you’re observing is a result of the projection used to display the map on a 2D screen. They actually do use pentagons to solve the tessellation issue.