Bucky Fuller’s Dymaxion projection projects the globe onto an icosahedron (a 20-sided polyhedron) and unfolds it. Take the same principle, but project the globe onto a polyhedron of immense complexity, with a lot more sides, and you get a myriahedral projection, the subject of a recent research paper (PDF) in The Cartographic Journal by Jarke J. van Wijk. The following video gives some examples of myriahedral projections, some of which will make your head explode:

Via Infonaut.