This is the true reason for my previous project on Platonic Solids. I was playing around with map projections, and became a tag smitten with Buckminster FulIer’s Dymaxion Projection.

It’s able to do a map projection with surprisingly little distortion:

I laser cut the ‘gore’s onto wood tiles:

The vertices are sized to allow an M3 screw to hold without needing any nuts, or pointy self-tapping screws.

Files are here for anyone that wants to make their own:

http://www.thingiverse.com/thing:1871829

(Note: this is decended from this image here: https://en.wikipedia.org/wiki/Dymaxion_map#/media/File:Fuller_projection_rotated.svg

Made by Eric Gaba – Wikimedia Commons user: Sting)

I’m not sold on the Dymaxion being the default map projection for humanity, but it has some interesting properties, and it was certainly a fun build.