4 ms·

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.

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?

bloopernova 5y ago
They distort the hexagons as you go further north. https://observablehq.com/@four43/h3-index-visualizer https://observablehq.com/@four43/h3-index-visualizer https://imgur.com/a/SgDfJkG https://imgur.com/a/SgDfJkG is an example
- ritwikgupta 5y ago
  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.
robinhouston 5y ago
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/ https://eng.uber.com/h3/
ravar 5y ago
There are 12 pentagons conveniently placed over water. The docs are a pretty interesting read. https://eng.uber.com/h3/ https://eng.uber.com/h3/
- progbits 5y ago
  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 :)