Most people know that Earth's landmasses once formed single supercontinent, but how said continent peeled away from itself – or the extent to which Earth's continents remain connected – is not always immediately apparent. That's where the Dymaxion map comes in.
The Dymaxion map sprang from the mind of architect/inventor/futurist Buckminster Fuller. Writer Alvin Toffler once called Fuller “one of the most-powerful myth-makers and myth-exposers of our time… a controversial, constructive, endlessly energetic metaphor-maker who sees things differently from the rest of us, and thereby makes us see ourselves afresh.”Indeed, anyone familiar with Fuller, his ideas or his inventions knows he had a certain special way of looking at the world.
In the case of the actual, literal world, that way involved projecting it onto an icosahedron and unfolding it into two-dimensions to reveal the planet's continents as "one island" of near-contiguous land masses:
Fuller's is what is commonly called a compromise projection, a map that forfeits certain geographic parameters in favor of others (the popular West Wing scene featured here explores some of the tradeoffs made in the name of map-making).
Like other compromise projections, the Dymaxion map attempts to preserve the relative size and shape of the planet's assorted land masses, distortions the more common Mercator and Peters projections struggle with, respectively.
One particularly noteworthy feature of the Dymaxion map is its ability to be re-assembled and unfolded in a new configuration. Unfolding it in one way emphasizes the near-contiguous landmass featured above. Unfolding it another, however, gives you an icosahedral net with a global ocean surrounded by land.
According to the Buckminster Fuller Institute, Fuller worked on this map for decades before it came into being in 1954. When it did, he believed he had finally realized a "satisfactory deck plan of the six and one half sextillion tons Spaceship Earth." ("Spaceship Earth" being a wonderful concept that relates our planet to a spaceship flying through the cosmos.)
Tons more great info and resources at genekeyes.com, BFI, and this list of frequently asked questions about The Fuller Projection. And if you're feeling interactive, check out this Dymaxion Map puzzle (be warned: if you're into this sort of thing, this puzzle can turn into an epic time-suck).