Authagraph World Map turns the Earth into a rectangle using tetrahedrons

Описание: Most common world maps are highly size distorted, with any land masses located toward the poles tending to look much bigger than they really are, which, in some ways, makes this weird-looking projection a lot more accurate. How it's made is a fascinating process – now, what is it actually useful for?

Creating 2-D maps of the entire Earth is a hard job. It's a sphere, and trying to nicely unwrap it into a neat rectangle leads to varying degrees of distortion. The map you're familiar with, that pretty much everyone has a copy of somewhere, is called the Mercator Projection, which was first presented by cartographer Gerardus Mercator in 1569.

It works well for nautical navigation, but it also massively distorts the size and shape of land masses, particularly near the poles. Take Canada as an example – it looks absolutely enormous, but if you remove the cylindrical distortion, you find it's not actually that much bigger than Australia (if you don't consider an extra 2.3 million km2 (888,000 mi2) much).

There are many more, and now another has joined the list. Winner of the Japan Institute of Design Promotion's Good Design Award for 2016, meet the Authagraph World Map.

Clearly, nobody is using this thing to plot a course. Lines of longitude and latitude bend, twist and curl, and figuring out which way's north is a challenge in some spots. But in terms of representing the size and shape of land masses, it's actually very accurate.

Created by Hajime Narukawa of the Keio University Graduate School of Media and Governance, the Authagraph map fits perfectly into a nice rectangular shape with a neat 3:4 aspect ratio thanks to its ingenious method of construction.

First, the sphere is divided into some 96 regions and then these regions are mapped onto an inflated tetrahedron shape. The inflated tetrahedron is flattened into a regular tetrahedron, then the tetrahedron is cut out and flattened into a big triangle and lined up with a whole bunch of other ones. From there, you can choose where to cut your map out from, depending on what you need to highlight and whether you're comfortable cutting land masses in half.