It's easy to deal with the way locations interact on a clean Cartesian grid. It's just vanilla math. And you can kind of ignore the geometry of the sphere's surface for a bunch of it if you want to just truncate the poles or something. But I keep coming up with ideas for games where the polar space matters. Geo-coded ARGs and global roguelikes and stuff.

I want square(ish?) locations -- reasonably representable by square tiles of the same size across the globe, anyway.

This has to be a solved problem, right?

What are the solutions?

ETA:

At the equator -- and assuming that your square locations are reasonably small, it's close enough to true that you can get away with having one square in the rows north and south of the most equatorial row. And you could probably get away with that by just hand-waving the difference up to like 45-degrees or so. But eventually, you need to have fewer squares in a pole-ward circumferential row. If I reduce the length of the row by one and offset the squares by 1/2 then they're just like hexes and it's relatively easy to do the coding to keep track of the connections. But as you get pole-ward, it gets more and more extreme.

Projecting the surface of the world onto the surface of a cube is tempting. But I figured there must be more elegant solutions already in use.

If I did the cube thing (not dissecting it further through geodesy) Are there any pros and cons related to placing the pole at the center of a face or at the vertex of three sides?