Hello! I’m Peter!
Blog
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LEGO Truchet
In the process of going through my old saved tweets as I transition away from Twitter, I saw this tweet from Dave Richeson who is now posts on Bluesky as @divbyzero.bsky.social. About one year after this, I made a LEGO Truchet tiling for Dave, not realizing that I had probably been unconsciously inspired by his!
Mastodon
Recently I saw a post on Mathstodon from @diamabolo, which goes a step further: a LEGO Truchet Tile Machine!
Stud.io
When I went to make my own LEGO Truchet, I used LEGO Studio to make some digital mockups, find the part numbers, and by the pieces in bulk via Bricklink.
LEGO Truchet in the physical world
I ordered 172.46€ worth of parts from Germany—enough to make eight different tilings, three of which are shown below.
Building for Dave Richeson
One tiling was based on a post by Dave Richeson’s bot @randomtiling.bsky.social, which I mailed to him. Here’s a picture of the work-in-progress.
The design was based on an actual post from Random Tiling Bot (@randomtiling), which I can’t find now. This one is close enough:
LEGO part numbers
The 10 x 10 Truchet tiling I made for Dave is made from two different LEGO parts together with a 32 x 32 gray baseplate.
- Part 25269 — Tile, Round 1 x 1 Quarter
- Part 3396 — Tile, Modified 2 x 2 with 2 1 x 1 Curved Cutouts (Double Arrow)
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“A beautiful little problem!”
I’ve been going through my old Twitter saves, when I came across this one which was no longer available, but which intrigued me!
The post is now gone from Twitter, but I found it via the WaybackMachine.
Prove that if all the coefficients of the quadratic equation \[ax^2 + bx + c = 0\] are odd integers, then the roots of the equation cannot be rational.
Want a hint for solving the problem? Highlight the following hidden text:
Write down \(1^2, 3^2, 5^2\) and \(7^2\) mod \(8\).
Use this together with the quadratic formula.
This problem comes fromThe USSR Olympiad Problem Book (1962) by D. O. Shklarsky. The whole book can be found digitally on archive.org.
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Hinged stellated dodecahedron
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:
