Photo by Gavin Smith

I was playing around with map projections one day and became a tad smitten with Buckminster Fuller’s “Dymaxion” Projection. It’s able to unwrap a spherical map of the Earth onto a flat plane with surprisingly little distortion. The flat Dymaxion map can then be divided up into triangles and folded back into a three-dimensional figure. I started this project because I wanted to make my own 3D version of Fuller’s globe.

What’s a Dymaxion globe, anyway?

When you think of a conventional flat depiction of the world, you’re probably imagining the classroom-mainstay Mercator projection, which dates way back to 1569: a flat grid with the Americas on the left and Europe, Asia, and Africa on the right. Its grid structure was a boon for navigation, but flattening out the map introduced massive distortion, to the point where Greenland is almost the size of Africa and Antarctica is a thin line at the bottom.

The Dymaxion projection, as developed by Buckminster Fuller, creates a flat map of the Earth with less distortion to the size and shape of landmasses. The map also doesn’t have a traditional up and down, and the flat sections can be shifted around to show various configurations of the continents that are all accurate.

Trial and Error

My first thought was to laser-cut miter joints into the panels and glue them together, but this led to big seam lines on the map, and it was hard to hold all the pieces together while gluing. Next, I decided to make a row of holes and tried sewing the faces together. The stitching was a bit time consuming, and it was difficult to retighten the stitches if the thread came loose.

Finally, I had the idea of using 3D- printed vertices, and using screws to hold the tiles (Figure A). I printed the vertices in ordinary PLA and sized them to let M3 screws self-tap nicely into the plastic.

Figure A-1. Photo by Hep Svadja
Figure A-1. Photo by Hep Svadja
Figure A-2. Photo by Hep Svadja
Figure A-2. Photo by Hep Svadja

With a bit of playing around with angles and parametric design, I made vertices for all five Platonic solids, including a tetrahedron (4 faces), cube (6 faces), octahedron (8 faces), dodecahedron (12 faces), and an icosahedron (20 faces) for the Dymaxion globe (Figure B). You can download the files.

Figure B. Photo by Gavin Smith

Hooray for Technology

I downloaded the Dymaxion map as an SVG from Wikipedia (Figure C).

Figure C. Photo made by Eric Gaba – Wikimedia Commons user: Sting

It took about an hour’s work to get something suitable for laser cutting (Figure D). It wasn’t perfect, but it was way better than tracing manually with a pencil and paper. You can download my DXF file. I made it in a hurry, and you may notice I didn’t bother to fix the broken triangles in the file, and instead glued them together after cutting. Thingiverse user Kim Stroman (“kbst”) remixed my version and stitched together the triangles, so you may want to start with her version.

Figure D. Photo by Gavin Smith

There’s a bit of a dark art to my laser cutter, so when I imported the DXF file all the lines came in as black. I had to select the lines by hand in the laser software and chose whether to cut or engrave. This was time consuming, but once done you can save the file in your laser cutter’s format and use it again easily. Other laser cutters are hopefully much smarter than the one I used. You should experiment and see which (if any) works for you.

Get Creative

I used 2mm–3mm bamboo ply for the triangle panels and a Copic marker to color in the continents by hand (Figure E). This was mostly because I was in a hurry and didn’t want to edit the file too much. However, you could also engrave a solid fill with the laser and save time. Alternatively, you could also get creative and paint both the lands and waters in much bolder colors, or water down the paint to create a subtle wash on the wood, which preserves the original grain.

Figure E. Photo by Gavin Smith

I’m pretty happy with the construction method. Sure, it’s not exactly light on screws, but I rather like the aesthetic of the cap heads, compared to countersunk or dome heads. Plus, it’s extremely strong. I can stand on the map, and it takes my weight with no problem!

Also, the nice thing about this approach is that the vertices work for any tile that has the hole 15mm from the edge. To make a larger object, all you need to do is recut the wooden parts and the 3D-printed vertices can stay the same.

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.

Going Further

To more easily show off the transition from flat map to globe, consider using magnets to hold it all together. A chap called Stefan Daschek got in touch and let me know he made a magnetic foldable version.