An ounce of application is worth a ton of abstraction.
Here is an
icosahedral projection of Earth and a blank sheet that will help the discussion. WARNING: LARGE PICTURES! You may want to download them and use something like ACDSee to reduce their size to fit on your screen.
This
free view of Earth in 3D is much better than the link Capitan tried to shleff off on you. Not as fancy, but it's still beautiful.
Anyway, back to the ico-Earth discussion. As the pictures show (well, except 5 and 6, where I colorized the edges and it looks like crap), a whole globe can be split into 20 large triangular areas, each of which, at its point, forms a pentagon arrangement with 4 other triangles. These large triangles can be divided up into as many hexes as you like. In Pic #4, you can see that the base of each triangle is 8 hexes wide, meaning that each hex gives a diameter of about 1000km (600 miles), or about 10 degrees at the equator. Each hex can also be divided up however you like, such that each tiny hex might be like 10km across, giving each large hex a diameter of 100 hexes. With 640 of these hexes on this map, and 750 10km hexes each, this gives a large area.
Note: I am treating the pentagons as hexes for all intents and purposes in the above figures. Additionally, I wouldn't dream of inflicting 480,000 spaces on a gamer, but some one else might.
I know pics 5 and 6 are a bit ugly, but I have since made a much MUCH better version of this map; I just haven't posted it yet, nor have I posted a sub-divided hex, which I described above. (This may change in the near future.)
In the game, I would expect the computer to "cut out the ico-projection and fold it into a D20 shape and always display it that way". Naturally, when I have to look at an edge or corner, the computer will flatten that part out a bit so it doesn't look so distorted.
Alternately, if the world is divided into enough triangles, and we use the TRIANGLES as the spaces, well, there's ALWAYS only 3 directions to go then, even when occasionally we find 5 triangles grouped together instead of 6. Pic number 7 gives just the barest glimpse at what this might look like.
On the other hand, the team COULD go with a radial-projection coordinate system. This would be a longitude angle and a distance from the north pole. The computer will have to reemmber that as one gets closer to the pole, a mile covers more degrees of longitude than it does at the equator, so the range of 100 miles for my Harpoon missiles will go 100 miles no matter how many degrees of longitude it winds up being.
The gains to be made from using a globe are impressive. First, we can FINALLY make an accurate projection of the Earth! Second, we can play on Mars or Venus if we want, or even the Moon; we just import radar altimeter data from a space probe and then tell the game what sea level is. We might even get to watch it while we adjust the elevation, looking for just the right amount of land and sea. And thirdly, there will finally be no more overwhelming advantage to being placed in Asia, with it's ridiculously oversized distortion of its landmass. Heck, even the Pacific might be a challenge to cross!
And since you should all be using a mouse by now anyway......
