# Simon’s Magnum Opus

At the beginning of each year, I make a very long, ridiculous video (which I like to call a “magnum opus”). Last year it was the 2048 cookies project. This year, it got so long that I had to split it into parts. In this video (parts 1 to 4), I set up to prove that there are 13 Archimedean solids. Link to my text file with valid and invalid corners: https://repl.it/@simontiger/ArchimedeanSolids#corners.txt

In the second video, I prove that there are 13 Archimedean solids by actually building them. No, the construction set I used in this video (Geomag) did not sponsor me 😄

Simon’s proof has been featured on The Global Math Project 🎆🎇

Simon had been working on this proof for many days. At first he didn’t know where to start, he only knew he wanted to prove that there can be only 13 Archimedean solids by building them with Geomag. He then came up with the idea to write a Python code that would search for all the possible corners that solids could have. It was a project in its own right to come up with a good algorithm for such a code! And after his code delivered a little over 120 possible corners, Simon started building solids with those corners coming up with logical arguments to eliminate invalid ones along the way. For example, he discovered this general rule to build an Archimedean solid:

Geomag has been ruling the house for a while here, allowing Simon to both explore shapes and electromagnetism in a tactile way and just try out some architectural concepts:

The above shape looks like two pentagonal bipyramids combined but they’re not! That’s because the height of a pentagonal bipyramid is not the same as its length, it’s actually slightly longer.

Reading up on why triangles make stable constructions and why truss is better than beam in our currently favorite bedtime book, Math with Bad Drawings by Ben Orlin.

And this is probably the closest we’re getting to New York this year, Manhattan Bridge and Statue of Liberty visualized below (our trip booked for May last year got cancelled) 😏