[nollidge]

I've thought about trying to build an app that does what that animation on the Wikipedia page does [0], but I'm not sure where I'd find spherical (or near enough) textures of the world map to experiment with.

[0] http://en.wikipedia.org/wiki/File:Dymaxion_2003_animation_sm...

[jre]

You could "unproject" another projection for which you have texture back to your sphere and then do the isocahedron projection.

Also, maybe you can find a database of the countries border as lat/lng polygons and just draw the countries.

[sampo]

Natural Earth has lots of that kind of databases: http://www.naturalearthdata.com/downloads/