a) Whats the name of this projection? enter image description here


b) Is it possible tu use this projection in qgis?


From a quick browse in wikipedia, it looks like this:


however, I would contact the author of the article to confirm it, as there is no indication on the map or in the article regarding the projection.

Regarding QGIS use read (spoiler alert: there are intellectual property issues involved):

Dymaxion/Butterfly alternative projection for QGIS


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