How it works
Put a light at the centre of the globe and a cube round it: each point casts onto one of six faces.
That is the gnomonic projection, six times over, and it is how
S2 starts. Unfold shows it: the globe swells to the cube, then
the cube opens into a staircase of faces 0 to 5.
Gnomonic cells are much bigger in the middle of a face than at its corners, so S2 stretches each
face with a quadratic before cutting it into a grid. Tick "Without the stretch" to see the
unstretched grid. Each level splits every cell into four.
The cells are numbered along a Hilbert curve that runs through face 0, then 1, and on to 5, so
cells close in number are close on the globe. A cell's id is its face and its path down the
curve; the token is that id in hexadecimal without its trailing zeros.