I've always been interested in maps and different projections and how they make such a difference in the way the world looks when a sphere is projected onto a flat surface.  Yesterday my wife sent me this link to an issue of Life Magazine from March 1, 1943.  On page 41 of this issue they discuss a new (at the time) projection from Buckminster Fuller, a famous inventor who is now most well-known for his geodesic spheres and houses made out of them.  This projection is called The Dymaxion World, and can be folded up to form a geometric object known as a Cubeoctahedron.  While the point of the projection is to have a flat-map with desirable properties such as low distortion and the ability to have all of the landmasses contiguous, I just think it looks cool folded up to form a bizzare globe.   Note: Fuller eventually decided on another polyhedron, the icosahedron, to use for The Dymaxion World.  It is a much "rounder" shape that actually looks like a globe. I've made those before and I don't think they look nearly as cool.

The images of the templates at the very bottom of this post, obtained from the original article, are high enough resolution to make about a 10 inch globe on standard paper if you click on the pictures and download the higher resolution version.  I used thick cardstock, and a tacky glue to construct mine.  All you have to do is glue Tab A to Tab A, Tab B to Tab B, Tab C to Tab C...

Here's a picture of the one I built: