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I've been reading the Dymaxion and Butterfly projections are not open source, so can not be used with QGIS.

Are there alternatives to these available in QGIS?

I'm looking for a single projection so I can export relatively-accurate SVG shapes of countries around the world when I need them.

It's important these countries are relatively-close to the way they would appear on a globe.

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Proj.4 knows the Icosahedral Snyder Equal Area projection +proj=isea, but not the inverse projection. For that reason, it is not usable by GDAL.

I guess the Waterman Butterfly projection will fail for the same reason.

Waterman butterfly projection in Mapnik lists some alternatives.

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