Math + Making

A student blog for Math 189AH: Making Mathematics at Harvey Mudd College

wallpaper groups box!

Nora O’Connor

For this project, I wanted to build a small wooden box using the HMC wood shop (which I’d never been to before!) and then illustrate the 17 wallpaper groups on it. The wallpaper groups are a group theory concept. A wallpaper is a repeating image that can cover a plane. It has certain isometries that preserve the pattern There are 17 unique wallpaper groups, shown below.


The first group is very simple and is only composed of translations. As the wallpapers become more complex, we see reflections, rotations, and glide reflections in addition to translation.

I found this super fun website that was helpful in understanding the types of symmetries present in the wallpaper groups:

To begin this project, I first had to learn the necessary tools in the woodshop. My shop proctor friend (thx emily!) showed me how to use the chop saw, tablesaw, and bandsaw. I immediately got a piece of wood stuck in the chop saw which was a little embarrassing.

After that, I bought some wood at home depot, and found a plan for making a box that I liked. I attempted to follow the instructions on this page:

I started by cutting my wood into planks the size I needed. I then made small grooves in it for the top and bottom pieces to fit in. After that, I made 45 degree cuts on the edges so I could fit it all together and attach everything with wood glue.

This was all pretty difficult and took way longer than expected. I think doing it again would be much easier, but the first time was rough.

Because I was slightly too scared to return to the wood shop, I next decided to work on coming up with some tilings. I used the website I linked above to create and SVG file of a pattern I wanted. (shown below)

My next steps will be fixing up the box, and then laser cutting this on one of the sides! After that, I’ll see where I’ll go with adding the rest of the tilings!



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