One of the earliest laser cutting projects I ever considered was when I was a graduate student: making a stellated dodecahedron. When I got to Harvey Mudd College and had the opportunity to use the laser cutter in the Makerspace for the first time, it was one of the first things I attempted.
My initial method for securing the faces together didn’t work very well, so I ended up using the pieces and some Scotch tape to hold it together (with lots of tissue in the inside for some added structural integrity!)
On my second iteration, I bought some small hinges in bulk for 8¢/ea, and used a hinged construction. (I believe these are the same hinges that Alex Kontorovich used in his excavated truncated cuboctahedron in Polyplane.)
Here are some photos I made of the build process.
In order to make two stellated dodecahedra from one laser cutting process, I nest the shapes like this. The outer face results in a see-through polyhedron like the piece of mine that was in the Mathematical Art Exhibition at the 2025 Joint Math Meetings.
The inner face makes a solid stellated dodecahedron like the one shown in the construction pictures above.
You can find the SVG code for this here, if you want to run it on your laser cutter:
<?xml version="1.0" encoding="UTF-8"?>
<svg width="200" height="300" version="1.1" style="fill:none; stroke:#00AA00;">
<circle cx="122.17231" cy="113.39211" r="2.5"/>
<circle cx="108.57557" cy="155.23862" r="2.5"/>
<circle cx="86.340271" cy="155.23862" r="2.5"/>
<circle cx="72.74353" cy="113.39211" r="2.5"/>
<circle cx="75.5" cy="27.5" r="2.5"/>
<circle cx="119.5" cy="27.5" r="2.5"/>
<circle cx="154.5477228333333" cy="76.21576816666669" r="2.5"/>
<circle cx="140.9509748333333" cy="118.06227616666669" r="2.5"/>
<circle cx="54.049025166666674" cy="118.06227616666669" r="2.5"/>
<circle cx="40.45227716666667" cy="76.21576816666669" r="2.5"/>
<path stroke="#FF0000" d="M 10 10 L 185 10 L 97.5 279.297 Z"/>
<circle cx="75.5" cy="57.5" r="2.5"/>
<circle cx="119.5" cy="57.5" r="2.5"/>
<path stroke="#FF0000" d="M 40,40 H 155 L 97.5,216.96662 Z"/>
</svg>Here are some more pictures of the piece that was in the 2025 exhibition:
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