Flexify (http://www.flamingpear.com/flexify-2.html) is an incredible decades-old Photoshop plugin for making these. I made a mobile for a grade school math project using Flexify and NASA's equirectangular planetary maps, turning Mercury into a tetrahedron, Venus a pentahedron, etc.
The gallery of output projections is neat: http://www.flamingpear.com/flexify-output-modes.html
The author of Flexify is
https://news.ycombinator.com/threads?id=lloydb
That's slick. I use papermodel+Blender for my models, but I haven't bit the UV mapping bullet yet!