The AuthaGraph map projection projects the Earth's surface onto a triangular pyramid which is then unfolded and transformed into a rectangular map. The size and position of the continents and oceans are much more accurate while preserving a rectangular shape for ease of use — and our comfort, that maps are usually rectangular. Its designer, Hajime Narukawa, won a 2016 design award in Japan for this effort.
I just think it is neat. I've tried using the Dymaxion triangular projection but it just looks so weird that it distracts from the point it is trying to illustrate. People instead get lost in the sharp edges of the map. It looks dangerous.
Inovative map projections which do not exaggerate the land area of Canada and Greenland seem especially relevant right now.