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?...
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.
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.
What "size problems" are you referring to? The Peters projection really is equal-area. When you say "size" are you referring to something else, like shape?
But the Peters projection is a lot easier to read with the expectations most people have for the word "map." The Dymaxion map illustrates to me why it's not always best to solve for a single variable without making any concessions elsewhere. You have something that works really well for that one problem, but it potentially becomes unusable in real life.
Dymaxion map is beautiful. But I consider it critically flawed for "general use". Understanding the distances between points on Dymaxion map is nigh impossible (at least for me).
I think Bucky's point was to show the world as a single continent. Kind of subverting the cold war a bit by showing our continents in closer proximity, and emphasizing our common interests. He also envisioned a worldwide electrical grid that would span the North pole.
This projection looks fantastic. It would b great if people actually started using this in schools and what not. With the advent of tablets and the general digitsation that's been going around, you can have "rotable" Dymaxion maps -- maps that could be rotated and oriented in such a manner as to look like what we're used to -- but when zooomed out, the Dymaxion/Fuller projection gives students/people an accurate picture of what the earth truly looks like.
If only they made real life rotating, oriented maps. They'd need a new name, perhaps something emphasizing their roundness...balls? No, the kids would make fun of that. Spheres? Too generic.
Good point. I think real life globes would take up too much space though. On the other hand, Google Earth looks like it does a good job depicting everything in proportion.
http://en.wikipedia.org/wiki/Dymaxion_map
If you are interested in a size-accurate map, you can't get much better than that.