Most of the time, laser-cut polyhedra are made by cutting individual faces and, attaching them either to each other with connectors or, to a base internal structure. I had an idea for a different way to do it based on paper craft polyhedra.

The general idea is to laminate the material for the faces to a heavy card stock. Then, cut through just the top layer and enough to score the card stock so it folds nicely.

This works great with all kinds of outer layers, including different card stock, wood veneer, shell veneer, cork, fabric, etc.

I found some fast-drying PVA-style glue that sets up fast enough to stand while assembling them (about a minute).

Another challenge of paper polyhedra is that it is difficult to get the final tabs to stick well as it’s not possible to push on both sides of these. I solved that by cutting out the last side and, just leaving a frame. That way, I can get a finger or a tool inside (depending on size) to push against both sides. By removing the laminated outer layer from that frame side, I can then put a solid panel over it to hide the opening.

Since the resulting polyhedra are hollow, it is also possible to put a light inside. I designed a little triangular Celtic-style key pattern and, cut a latticework into each of the faces of an icosahedron. I added an interior vellum backing layer to act as a diffuser. I built a couple different circuits using CR1216 coin cells and Chibitronics Circuit Stickers. The second version uses a reed switch so the light can be activated with a magnet from the outside.

I have made a bunch of these and, will likely make more in the future.