From the press release:
"Myriahedral projection" was developed by Jack van Wijk, a computer scientist at the Eindhoven University of Technology in the Netherlands.
"The basic idea is surprisingly simple," says van Wijk. His algorithms divide the globe's surface into small polygons that are unfolded into a flat map, just as a cube can be unfolded into six squares.
Cartographers have tried this trick before; van Wijk's innovation is to up the number of polygons from just a few to thousands. He has coined the word "myriahedral" to describe it, a combination of "myriad" with "polyhedron", the name for polygonal 3D shapes.
Check this out: You can try to fit the earth's surface on unfolded nets of different shapes.
The new algorithms though go a step further. The nets have many more sides and are shaped more intelligently in ways that arrange continents and oceans in different configurations but with minimum distortion to their shapes where they are cut and unfolded.
For example here the oceans are one continuous expanse surrounded by coastlines
You can see the rest of the maps at this picture gallery
Jack van Wijk won the Cartographic Journal's Henry Johns award for the best map-making research paper of the year.