In the Goldberg polyhedron used in H3 {5+,3}_{a,b} with {a,b}={2,2} or {8,2}, the pentagon area to hexagon area ratio is of about 0.66.
Do you know a way that I can modify a little the pentagon shape (and by conscequences the 5 coniguous hexagons of the 12 pentagons) in such a way that, the area ratio of any couple of tiles is better close to one?
In my application I both needs tile shapes close to a circle, and the ratio of of any couple of tiles close to one as much as possible (ie. I am penalized even by a very small amount of small tile area ratio)
Best Jean-Eric
I don't think this is possible using H3. You cannot change the shape or coordinates of cells, at least within the library itself, as this would undermine the consistent indexing of points in the grid.
H3 aims for roughly equal-area cells, but there's still a significant amount of area distortion across the grid, particularly at coarser resolutions. See https://observablehq.com/@nrabinowitz/h3-area-variation for a visualization of area distortion at res 0-3. Even if pentagons were removed, the cell distortion between the smallest cells (the pentagon neighbors) and the largest cells (at the center of the icosahedron faces) is almost 1:2. This is a function of the projection of the planar hexagon grid onto the sphere (we use a gnomic projection for each face).
Depending on your use case, you may be able to correct for this by weighting data according to cell area. At present, you'd need to use an external library to calculate this, but we're in the process of adding area calculation directly to the library.