By Sam Hume
Even as the technology and methods used by cartographers to map the earth have improved over time, they still face one insurmountable obstacle in creating their maps: How to represent a three-dimensional object in two dimensions?
No matter what decisions they make there must always be tradeoffs, because when you remove a dimension you are removing essential information. For this reason all maps suffer from distortions in accuracy. These distortions are most commonly found in: distance, direction, area, and shape.
When creating a map, cartographers must decide what the map will be used for and based on this, they will focus on minimizing the distortion in the factors most relevant to the map’s use case. The (in)famous Mercator projection was designed for use at sea and so preserved direction (or bearing) allowing for navigation across most of the world.
The Mercator projection was devised over 400 years ago! Since then, cartographers have been hard at work designing new and better projections as well as some more strange ones. One interesting attempt to capture the 3D world in 2D is the polyhedral projection. A sphere is an extremely complex shape to represent in two dimensions. What if we simplified it a bit first?
The polyhedral projection type attempts to do this by first simplifying the sphere of the earth (more accurately an ellipsoid) into a polyhedron, a 3D figure made up from a set of 2D faces. Think something like a soccer ball or cut gemstone. From here we can simply extract each face and stitch them together into a flat surface. Sure there will be empty gaps, but maybe this way we can get a less distorted map?
The projection in the image is an example of a polyhedral projection, it is designed to preserve the relative area of all continents (except Antarctica) as best as possible, allowing us to compare them. It is based on the famous butterfly polyhedral projection created by Bernard Cahill, and was first implemented by Luca Concialdi in 2015. It’s important to note that this projection is not free from areal distortion but does its best to minimize it equally across all continents except Antarctica.
What makes polyhedral projections so interesting in general is that they can be seen to be an “unfolding” of the 3D earth into a flat 2D map. If we were to cut up a print of the Cahill-Concialdi projection we could probably assemble a decently accurate globe of the earth!