3D printers are ace. People are using them to make all sorts of cool things. If you can describe a shape to a computer, it’s very easy to send that description to a 3D printer, which will happily smoosh some substrates together to make a real model of your shape. Mathematicians are able to describe all sorts of crazy shapes, in exactly the amount of detail computers need, so they’ve taken to 3D printing like ducks to water.

Thingiverse is just a repository for designs, so if you see something you like you’ll have to find your own 3D printer. Shapeways makes the objects and posts them to you; prices can vary from just a few euros to hundreds, depending on the size of the object and the materials used.

As with all other kinds of mathematical art, there’s a huge amount of repetition of the same few ideas, but also a few really interesting and unique designs. I’ve picked a couple of representatives from each of the popular topics, but do search around if you want a version with slightly different parameters; you’re bound to find something suitable.

For the past few months I’ve been quietly compiling a list of interesting mathematical objects I’ve found on the main 3D printing catalogues, Thingiverse and Shapeways. With Christmas approaching, I thought now would be as good a time as any to share what I’ve found.