How to fill globe nets with a map

Hello all.

For a week, I've researched and spoken to graphic artists, trying to figure out how to fill the nets for a placing on a sphere. There are templates for the nets online, but we/I cannot figure out how to distribute the image/map inside each of the nets, where the map is evenly and fully distributed in each, to then cover the sphere. This is a special project for a gift, I've the image/map that I designed and want to cover the sphere, ultimately to be a bespoke globe. 

I should mention that I am not a graphic artist, or an expert on different creative software, but do have all apps in the Adobe Suite and use Illustrator a lot. So I turn to you brilliant folk. 

Thanks for any ideas and/or ways to remedy this annoying problem greatly appreciated.