A 242-Sided Zonohedron

Was flipping through Zome Geometry looking for a project for today and found a really cool picture at the end of Unit 14. The shape – a 242-Sided Zonohedron – was described as “the largest convex polyhedron you can build with red, blue, and yellow struts.”

This was a doubly nice description since our green struts haven’t made the move up to Boston yet!

Interestingly there was really no further description, and no instructions on how to build it. Seemed like a nice challenge, though, and perhaps also a lesson in perseverance. So, off we went:


Building this object was a struggle right from the start. Luckily my younger son noticed that there were 10 sided shapes and 12 sided shapes. We know how to build decagons out of blues, so here was the beginning of our first build:


But we got stuck after a while – as the shape curved up, it wasn’t forming the same shapes that we saw in the picture. Quite a puzzle:


Our next try felt right. The only surprise is that the shape is absolutely huge. I was proud of the kids for figuring out that we could use other zome pieces for support struts. If you look carefully at the remaining videos, the support struts became more and more eloborate:


The next video comes when we are about half way through. It is fun to hear the kids talk about the shape – especially the “almost squares.” It seems as though we are building the right shape now, so that’s good. We broke for lunch and a little shoveling after this video since we’d been building for about an hour already.


Now for the big finish!! My younger son is actually standing inside the shape in this video. It was fun to build and you can hear their enthusiasm as they talk about it. This video also shows why I love building shapes with our Zometool set – there are so many opportunities to hear kids talking about pretty advanced math concepts during (and after) the build.

For just a little throw away comment at the end of Unit 14 of Zome Geometry this was quite a project!