Alright, idea time: It's not possible to create a grid consisting solely of hex tiles, which conforms to the curvature of a sphere, does not overlap itself, and completely covers the sphere's surface. However, it's very possible to create a grid consisting solely of hex tiles, which conforms to the curvature of a sphere, and does not overlap itself. As such, you could make a Pangaea map from this, featuring a single supercontinent and no islands more than two tiles out. The hex grid, which dictates movement and territory and all that strategy stuff, is limited to the area of the sphere occupied by the supercontinent and its nearby coastal/sea tiles. The ocean would be gridless. But wait! If the ocean has no tiles, then how would you be able to cross the ocean?? Well, ocean-faring units would have special movement rules. When on coastal tiles or inland seas, they move the standard, tile-based way. However, you can also direct ocean-faring units to sail off the edge of a continental grid, and they will sail blindly off into the uncharted waters, reappearing a few turns later across the pond. Alternatively, you can command an ocean-faring unit to sail to a previously-uncovered coastal tile (this will also take several turns). Combat would be handled in a manner similar to air units from Civ 4; ships can attack other units and districts in a short radius without moving from their stationed tile, and also be set to intercept any attacking naval units. (Of course, all these mechanics would then carry over to air units as well.) So you see, we've been going on about this all wrong. We don't need to try to think up some magical, mathematics-defying way of creating a spherical hex grid. We just need to tile the part of the sphere with dry land on it, and make the un-tiled oceans operate by different rules.