This week I was at a fancy dress-up event where they put things like cool flashing LED lights, watch batteries and pipe cleaners on the tables so all the guests could make stuff. It took me all of one minute to accidentally drop my watch battery, which promptly rolled somewhere far under the table, never to be found again. Which meant my cool flashing LED light would be useless.
And that left me with pipe cleaners. Fortunately, earlier that day I had been talking with Vi Hart, and I thought of her experiments in using household materials to make hyperbolic surfaces (seven equilateral triangles around a vertex instead of six, and you’re in business).
I started folding pipe cleaners into equilateral triangles, twisting them together so they wouldn’t fall apart. Except around every vertex I put five equilateral triangles. So instead of lying flat on a plane (which is what would happen if you placed six equilateral triangles around each vertex), the assembled triangles formed a slight curve.
After I did this for ten minutes or so, gradually adding new triangles, my little sculpture did what any self-respecting collection of equilateral triangles with five triangles around each vertex would do — it formed an icosahedron:
I put my little pipe-cleaner icosahedron on the table, and people were very impressed. Various other guests picked it up, played with it, and turned it this way and that. I suspect they didn’t realize that a shape like that practically assembles itself if you follow the right simple rule. And I wasn’t about to tell them how easy it is to make one of these things.
I did ask people if they knew how many sides it had. I’m sure that you, dear reader, will get the correct answer right away. Of course the next day I found myself surfing the web learning all sorts of things about icosahedra that I hadn’t known before. And I came up with an idea for another little icosahedron related project. More on that tomorrow.