http://en.wikipedia.org/wiki/Dymaxion_map
If you are interested in a size-accurate map, you can't get much better than that.
http://en.wikipedia.org/wiki/Dymaxion_map
If you are interested in a size-accurate map, you can't get much better than that.
I've always wondered, however; why not increase the density of faces (or vertices?) from an icosahedron, and have an even less distorted map? What would the monstrosity look like?...
[0] http://en.wikipedia.org/wiki/File:Dymaxion_2003_animation_sm...
Also, maybe you can find a database of the countries border as lat/lng polygons and just draw the countries.
In the limit, you could get something like http://en.wikipedia.org/wiki/Goode_homolosine_projection, but with infinitely many lobes. And that is a _could_: you can add branches like in Dymaxion wherever you feel like it.
Wait, I got it.
Let's call them globes.