Yay for the two D20 icosahedrons! I first thought I'd try to do mine on an origami waterbomb... but I couldn't figure out how to transform a projection I could think in, to a sheet of paper I could fold. Not that I've ever folded a very nice origami balloon. There is a real-world map out there on the interwebs to fold up and blow up, but the faces looked so scattered I didn't want to try. Carbus, you created that gorgeous map in 20 hours? Wow. What I get in 20 hours is usually about the crayon-on-paper-towel stage of beauty. I'm slooooooow. For such a work of art to also be pretty quick is double amazing.
But it just didn't wind up as a physical thing. Lingon, yours wound up spherical AND was a marvel of mappery, so you get my vote.
I'll put up a thread showing my experiment in a bit better form, after the voting's done. Basically, as far as my entry got, I proved to myself I need a substrate to mount the gores on. So I invested $1.68 in a standard kid's rubber ball, about 8 inches diameter, and I've been snapping some how-to shots. Thanks for the votes, y'all!