How it works
Put a light at the centre of the globe and an icosahedron round it: each point casts onto one of
twenty triangles, the gnomonic projection twenty times over. H3,
Uber's hexagonal grid, starts there. Its icosahedron sits where Buckminster Fuller put his for the
Dymaxion map, with all twelve corners in the ocean. Unfold swells the globe to the icosahedron, then
opens it into a strip: five faces round the top corner, a band of ten, five round the bottom.
On each face's gnomonic plane the hexagons are exactly regular, which is why they look so tidy in
the net and stretch a little on the globe towards the corners. Twelve cells can't be hexagons: at
each corner of the icosahedron five faces meet, so every resolution has exactly twelve
pentagons (outlined in orange).
Each resolution splits a hexagon into seven: a centre child and six round it, so cells are about a
seventh the area of their parents (aperture 7). Seven small hexagons can't tile one big one, so
children spill over their parent's edge (tick Children), and the grid turns by about 19.1
degrees at every step: even resolutions are Class II, odd ones Class III. An H3 index is its
resolution, one of 122 base cells, and one digit 0 to 6 per resolution saying which child to
take. Colour by "Last digit" to see the sevens.
The cells, their indexes and areas come from h3-js.
The icosahedron is built from H3's own twelve pentagons and numbered as H3 numbers its faces;
a test checks the faces against h3-js and that the hexagons are regular on each plane.
- H3: Isaac Brodsky and others at Uber, github.com/uber/h3 (Apache 2.0).
- Hexagonal aperture 7 grids, Class II and III: Sahr, White and Kimerling (2003), Geodesic discrete global grid systems, Cartography and Geographic Information Science 30(2).
- The icosahedron's placement: R. Buckminster Fuller's Dymaxion map.