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

Source:http://www.viewsoftheworld.net/?p=5737

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

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

https://en.wikipedia.org/wiki/Dymaxion_map

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

https://www.reddit.com/r/gis/comments/6t4f88/incorporating_dymaxionfuller_projection_into_qgis/

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