Wikipedia
Authagraph is an equal-area type world map projection that was invented by Japanese architect Hajime Narukawa in 1999.While conceptually in the category of an equal-area projection, it would require further subdivision to qualify as an actual equal-area map.
The Authagraph world map can be tiled in any direction without visible seams. From this map-tiling, a new world map with triangular, rectangular or a parallelogram’s outline can be framed out with various regions at its center. This map provides a decentralized world view. The map projection tries to reflect an infinite multiverse perspective that is intended to be of particular use for the understanding of global phenomena in the 21st century. The projection is uniquely useful for tessellation and thus allows for depicting temporal themes, such as a satellite’s long term movement around the earth in a continuous line.
This rectangular world map is made by equally dividing a spherical surface into 96 triangles, transferring it to a tetrahedron while maintaining area proportions and unfolding it onto a rectangle. The map substantially keeps sizes and shapes of all continents and oceans while it reduces distortions of their shapes at the same time as a Dymaxion map does. Triangular world maps are also possible. . The name is derived from authalic and graph.
In 2011 the Authagraph mapping projection was selected by the Japanese National Museum of Emerging Science and innovation (Miraikan) as its official mapping tool. As of 2015 it is used in official Japanese high school text books.