[scott_karana]

I was hoping to see someone post 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?...

[Someone]

To make it less distorted, you will have to make more cuts, seriously increasing the risk that the map does not accurately show the distance between points P and Q because the shortest path between them on the globe goes through a cut on your map.

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.

[scott_karana]

Thank you! :-)

[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/