Small Polyhedra

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.

Engraved wooden icosahedron — Icosahedron with wooden faces engraved with knotwork borders and numbers like a 20-sided die (~6cm / 2.25”)

Indigo ikat octahedron — Octahedron with faces covered with bits of a vintage kimono with a blue, white and, red ikat design (~8x5cm / 2×3”)

Sakura kimono dodecahedron — Dodecahedron covered with bits of a vintage kimono bearing a stylized sakura/cherry blossom design (~6cm / 2.25”)

Mother of pearl icosahedron (~6cm / 2.25”)

Copper key pattern lit icosahedron — Copper icosahedron with diffuser-backed panels cut with an original triangular key pattern design, lit from within by a yellow LED (~6cm / 2.25”)

Silver pulsing icosahedron — Silver icosahedron with diffuser-backed panels cut with an original triangular key pattern design, lit from within by a slowly pulsing white LED (~7.5cm / 3”)

Pewter red pulsing icosahedron — Pewter icosahedron with diffuser-backed panels cut with an original triangular key pattern design, lit from within by a slowly pulsing red LED (~7.5cm / 3”)

Pewter red and silver white pulsing icosahedra (~7.5cm / 3”)

There is a video walking through making a plain wood veneer dodecahedron and two lit icosahedra.

If you aren’t into videos, I did a write-up in a forum post with a little more detail about the process of making them.

If you want to try making some, here are the basic patterns for an octahedron (8 sides), a dodecahedron (12 sides) and, an icosahedron (20 sides). Let me know if you try this!

These files are for personal, non-commercial use only. Note that, by referencing these, you are agreeing to release any variations you create under identical terms.

Octahedron Pattern (SVG)