# On the twelfth day of Christmas, my true love sent to me…

twelve pentagons made from loo roll middles

If, like me, you stocked up on loo roll at various points during last year, and, like me, you don’t always remember to check the bathroom on recycling bin day, you may have ended up with a mountain of cardboard tubes that just cry out for a Blue Peter style craft project. Here’s something you could try. I saw a completed model using this technique ages ago on social media, and immediately decided I needed to reverse-engineer it and make my own models. I started making a dodecahedron and then ran out of loo roll middles and abandoned it in a corner to gather dust. It turned up when I was having a New Year Declutter and I realised I had plenty of raw materials (seriously, I don’t think I remembered to throw out a loo roll middle for the entirety of 2020), so I had a go at making something.

The pictures above show how to get started. Cut several toilet rolls into thin loops, around 3-5mm across should be fine. Then interlock three of them so that each loop goes over one and under the next, and then pull it tight as shown in the third picture. Now it’s decision time – what solid shall we make? I decided, rather ambitiously, to begin with a football, which (as Matt Parker famously got quite upset about once) are made up of a mixture of pentagons and hexagons. In fact, there are 12 pentagons and 20 hexagons, giving a total of 90 edges (or 90 little bits of cut up loo roll middle!) Mathematically speaking the football shape is a truncated icosahedron, one of the Archimedean solids.

I’m pretty pleased with the finished product. If you put a light in the middle, you get cool shadows too, but that’s really hard to take good pictures of, so you’ll just have to imagine it (or make your own!) As with other mathematical makes, I felt as though I understood the structure of the shape better as a result of figuring out how to make it. If you do decide to make your own, it’s quite a challenge to figure out how to get every piece but one into place (unfortunately the last piece does need to be cut and taped in order to close off the shape). Of course, if you’re doing it just for fun and you’re not so worried about using some tape, you could cut more sections for ease of assembly.