This started because I wanted to make my own copy of Buckminster Fuller’s  Dymaxion Map. Lasercutting mitre joints & gluing them leads to big seam lines on the map, as well as being hard to hold while gluing. Instead, I decided to make a row of holes and try sewing the faces together:

If you look closely, you can see the exact limit of my patience. 

But the stitching was a bit time consuming, as well as being difficult to retighten.

Instead, I had the idea of using 3D printed vertices, and screwing lasercut tiles into them:

With a bit of playing around with angles, and parametric design, I made the whole set:

Clockwise from top left: Icosahedron, Dodecahedron, Cube, Tetrahedron, Octahedron. 

I’m pretty happy with the construction method. Sure, it’s not exactly light on screws, but I rather like the aesthetic, and it’s extremely strong. I can stand on the icosahedron and it takes my weight with no problems.

Also, the nice thing about this approach is that to make a larger object, all you need to do is recut the wooden parts, and the 3D printed vertices can stay the same.

Files here for anyone that wants to make their own:

http://www.thingiverse.com/thing:1862570