Saw this incredible tweet from Laura Taalman a few days ago:
She’s created 3D print versions of all of the known pentagons that can be used to tile the plane!! The 15th pentagon was discovered in 2015, and that discovery is discussed by Evelyn Lamb in this amazing article:
I thought that the pentagons and tiling patterns would be really interesting for kids to see, so I spent the day printing the “cookie cutter” version of all 15 of them. Once the printing was done, we started talking about pentagons:
I had each of my kids pick a pair of pentagons to talk about – my son picked #8 and #13 (as numbered on Taalman’s program linked above). Here’s what he noticed about these pentagons:
Next, my older son talked about what he noticed about pentagon #5 and pentagon #9 – I was happy to hear him speculate about the possible tiling patterns formed by the shapes.
When I was printing the pentagons I happened to notice that #5 and #6 looked pretty similar. It turns out that there are two different ways to tile the plane with these shapes, so I did print out these tiling patterns. Luckily my son had picked #5.
It was fun to see that the 2nd tiling patter wasn’t totally obvious to the kids, but they figured it out eventually.
We wrapped up by playing around with the interface Taalman made for the pentagons. It is amazing to be able to see and play with these patterns. The boys played with it for 20 minutes after we finished filming 🙂
So, a super fun project. The great thing about 3D printing (and the thing I can’t say thank you enough to Laura Taalman for teaching me) is that holding these shapes in your hands leads to great conversations!