I built this lamp with laser-cut 3mm plywood and colored layer paper. I tested several designs since I first though for a simple way to build a geodesic structure. This model is finally too small to test this furhter but I kept thas wooden structure with paper glued on it.
Step 1: Finding the Right Angle
Each edge of the structure is a plywood stick with an angle wich allow the edge to group up against each other. I used a cad software to find that right angle : it is 121.718°.
Step 2: Holding the Edges Together
My first idea was to hold each edge against the other with a collar. The difficulty was to find a core to keep alignement nice an redular. Since I was trying to get a structure as precise as possible to be able to glue paper on it, the tolerances were very slight.
I cut some pentagons in 5mm plywood. It is still to imprecise and difficult to align.
I tried some thermoforming plastic but I've been unable to find the right way to shape it. Molds I tried to make were imprecise and the plastic was not flexible enough to get through a kind of pentagonal syringe I built.
Tapering each contact edge is certainly a good way to go but it seemed difficult to get a precise result on such small parts.
The best results were obtained with 3mm screws.
Since it was difficult to put everything in place while the collar was not tight, I cut some tools to keep each part in place.
Step 3: Using Connectors
I switched to connectors. They are 5mm plywood, the first model was a bit to big and I designed smaller ones. With connectors, building up the structure is very easy. I'd like to test the other method one day on a big structure but it would be a very different projetc.
Step 4: Faces
The faces are cut in colored layer paper. I also traced the lines for folding with the laser cutter. I designed the faces two by two because a larger piece would suffer from the imprecission of the structure. It's far more easier to glue dual faces than just one face. It needs to be very carreful to align them and avoid glue stains.
I tried to reproduce the distribution of the face of a true 20 sided dice but I failed. :( It's not far from it but it's not quite that). Maybe varnishing the paper could be a good idea. It doesn't seem to keep a nice finish with time.
The hardest task is to choose witch side would be sacrified to let the bulb to pass.
Step 5: Buidling Up the Stand
The stand is quite simple. The vertical parts are tapered to ensure the lamp to be centered. they also give space to let the wire pass.
I used a mild power bulb to avoid the lamp to be too bright.
Step 6: Files
Here are the svg files.