Creating a proportional map of the world is tricky because the world is a sphere and a map is flat. That creates visual distortions, which explains why Mercator projections shrink Africa and super-size Greenland. Designer Hajime Narukawa found a clever solution to this problem: triangles.
Narukawa’s AuthaGraph World Map, which recently won the grand prize in Japan’s biggest design competition, retains the proportions of the continents and oceans—so much so that you can fold it into a three-dimensional globe. Like magic! He achieved this by dividing the globe into 96 triangles and projecting them onto a tetrahedron, preserving the proportions of water and land. Then he unfolded the tetrahedron into a rectangle, where the 96 sections created a map resembling the surface of the original globe, only flat.
The general shapes of the continents are consistent with more familiar maps, but their orientation is not. On the AuthaGraph Map, continents curve upward like a smile. Africa and the Americas look like they swapped places. And longitude and latitude are no longer a tidy grid. But all maps require tradeoffs. You want an equal area map? Prepare for distortion. You want a Mercator? You’re living a lie. The AuthaGraph isn’t perfect—the creators concede that it needs “a further step to increase a number of subdivision for improving its accuracy to be officially called an area-equal map” the project creators write on their website—but it’s pretty damn close.