# Wrapping up a week of symmetry for kids by looking at an Icosahedron

I’m leaving for a Brute Squad practice weekend in Amherst, MA in about 30 min, so I’ll have to write this one up much faster than I’d like to, but . . .

Our little math project this week was looking at symmetries of the various platonic solids.  We had a lot of help from our Zometool set, too, and that made the project extra fun for the kids.  A write up  of the first part is here:

Studying Symmetry with Rubiks cubes and Zometool

Today we finished up the project looking at an icosahedron.  To start, though, I wanted to go through a quick review of some different ways to count the faces, edges, and vertices of the various shapes.   At the end I mention Euler’s formula:

Next we moved to the kitchen to talk about the symmetries of the icosahedron. After talking about symmetries for the 4 other platonic solids earlier in the week, my hope was that we’d be able to get through this exercise without too much difficulty. One thing that I learned during the week was that it was easier for them to see the symmetries if I held the shape while they rotated it.  The combination of holding, rotating, and trying to see the symmetries was just a little too much overload.

The conversation at the end of the last video about how the symmetries of the dodecahedron and icosahedron relate to each other was unplanned. Both kids seemed pretty interested in investigating the relationship, though, so we kept going. It seemed best to start by reminding them about the connection between the symmetries of the cube and the octahedron. Once they saw that connection again, seeing the connection between the icosahedron and dodecahedron was a little easier than I was expecting.

Studying all of these symmetries made for a really enjoyable week, and this very last video was a great (and unexpectedly fun) way to wrap it all up. Can’t say enough good things about the Zometool sets and how they can help kids see fun math!