
Photo by Gavin Smith

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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-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.
Very Cool, SteamPunk meets USGS Or National Geographic
My exact thoughts! This would go great on a desk with a Victorian lamp, aviator goggles, and a Datamancer-designed steampunk desktop computer outfit: https://datamancer.com/product-category/
My exact thoughts!
i think they look great just the way they are. especially with the round hex heads.
The 3D printed vertices are a great idea,
Dare I show my ignorance and ask what angle they are?
Since these are equilateral triangles the vertices must be 60 degrees. The sum of the vertices of any triangle will be 180 degrees. So here, 180/3 vertices = 60 degrees. “The only stupid questions are the ones unasked.” BTW tetrahemicon have you ever flown a tetrahedral kite? Being modular they can be quite big. Check out Alexander Graham Bell, he was a kite experimenter….as was Bucky.
I meant the angle between of the base and the faces of the purple 3D printed vertices, the little “penta-pyramids. It looks like less than fifteen degrees to me.
I never had any luck with rigid frame kites, but I had a great 18x 24 in ram wing that stuffed in a small sack. At the end of 1500′ of seemingly unbreakable string that kite in a really strong wind was just forced to the ground for want of more line. I couldn’t pull it in.
Ooops. I hope you took no offense at my stating what may be obvious. Can’t even guess on the angle you seek. It might be discernible by sectioning the 3D drawings. I learned the hard way that very thick gloves are needed for large kite work. I also still have an antique heavy steel wire (3/16″D.) clothesline winder that is great for the job.
I suppose an angle gauge would give an answer, I’m not enough of a geometer to calculate it on paper. I also can’t figure out an octohedron I downloaded from Thingiverse for 3D printing. It doesn’t sit flat on the build plate and when I rotate it there’s still a gap, like maybe it’s a half degree off. I had to slice a bit off to make it fully contact the surface. Maybe it’s inherent with the upload. I can’t understand why that pyramid’s face would have a fraction of a degree.
Yeah, I thought of an “Angle-ometer”. The link to a “kiddie math” site says 138 degrees 11minutes “under” the planes.
http://www.coolmath.com/reference/polyhedra-icosahedron
This site is so clear and direct. Others are too “rocket science” for me.
It gives me goosebumps to see the Now Generation being introduced to
Bucky Fuller, a visionary who I had the pleasure of chatting with for a
couple hours. Yes, the Dymaxion Projection results in the least land
mass distortion. Better too that it can be shipped flat, totally
understood flat, or assembled into 3D reality as Gavin Smith did in such
a cool way (stainless cap hex head or button head screws are my default mode). Some of Bucky’s writings are a bit tough to understand as
he was ahead of his time but worth a try. 60 years ago he was promoting recycling and
one of his favorite quotes was “Do ever more with ever less.” We are now
at the inflection point in history where his dreams can become reality
as long as we have the will to “Think (and act) Different”.
I was a big dome fan back in the day. My Dome Books 1 & 2 were worn out from use.
I never went “back to the land” far enough to get away from building code types though.
Only with the interweb did I learn of a guy building domes according to Bucky’s other dome patent – Self-Strutted Geodesic Plydome patent 2,905,113, They’re made from overlapping sheets of plywood with thousands of holes drilled and bolted together! Google it if you haven’t seen one. It looks haphazard with no symmetry. The neighbors would have loved the looks of that. Although it might not have leaked like some domes with struts and hubs.
Whole Earth Epilog, How to Keep Your Volkswagen Alive: A Manual of Step by Step Procedures for the Complete Idiot (by John Miur, really), How to Build Your Own Living Structures (by Ken Isaacs). These were in my collection at one time. “Idiot” books are not new. The VW one was self-published in 1969. Maybe we have shared interests?
Here’s a Bucky record (12″ vinyl LP) I found in a Milwaukee thrift shop long ago. Kinda sad that typographers had to step up and sponsor the album. But loved the STA for years because of their vision. https://uploads.disquscdn.com/images/d6b65bcd8ae6c6f57e3a639ad1924b5a7315bb8e7f2f693c26494f3bebb319f6.jpg .
Too bad “How to Build Your Own Living Structures” isn’t still in your collection, it’s going for $165 on Amazon. His name sounds familiar, but I don’t remember that book. I googled Isaacs & read that he worked for Le Tourneau heavy
equipment here in Illinois. I wouldn’t have thought Peoria was big
enough for anyone but Caterpillar. I probably saw him in the Whole Earths or Popular Science which he worked for. There was an obit from 2016 with a quote from him about living in a 4,000 sq ft home in later years. His answer was cute, but I can’t find it now. Fifty years ahead of his time with Micro-houses, but he lived to see the “Small Home” movement. But as always, the bureaucrats & their zoning ordinances and building codes are in the way.
The Bucky record you have is listed on Amazon, but unavailable.
A favorite of mine that I wish I still had was; “The $50 & Up Underground House book” & the $500 & Up sequel. “Earth sheltered” is the phase I went through after domes.
As for the 3D printed vertices above, I realized I could just download an icosahedron and cut everything away but that section.
How to Build Your Own Living Structures is available in pdf form for free at http://letsremake.info/PDFs/k_isaacs.pdf
Domes and kites are fine, but I have a soft spot in my heart for Bucky’s Dymaxion car, and even the Dymaxion bathroom, all in stainless steel! I finally realized he had a point about its durability and modern aesthetic, after owning four old houses and reaping the endless maintenance of traditional materials. Back to the car: I think Fuller would flip over the Tesla, and Elon Musk’s other ventures.
The Copic marker color and effect were a perfect, “classy” choice.
Sooo I’m about to show real ignorance here. What sized piece are you guys using for the laser? I think I’ve checked all the links but can’t find a part size for the laser cutting portion
Any tips on how to vectorise the images/convert into dxf? I tried to do that on illustrator but i could not get all the lines
Very super job, thanks! And just when I was about to say “magnets”, you mentioned Stefan.
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