At school my son is looking at polyhedra (that’s the proper word for polyhedrons – like cubes, tetrahedrons, etc).
The other day he came home with pictures of a dodecahedron (that’s the one with 12 pentagon sides) and an icosahedron (20 triangle sides). The icosahedron is really neat. Each point has 5 edges hitting it, and if you hold it right, you can have 5 sides in a top layer, 5 on the bottom, and 10 around the middle. It’s nicely symmetrical, and it feels familiar.
I think the reason it feels so familiar is because if you chop off the corners you get a truncated icosahedron. This makes each point into a pentagon (because there are 5 edges that meet at the point), and each triangle into a hexagon (because you’ve chopped each the corner off). Pump it up a little, and then you can play football with it. I think this should be called an ‘isoccerhedron’ though.
(Image is from the Wikipedia site)
The class didn’t actually look at the isoccerhedron, but I think the class full of boys would’ve enjoyed seeing such an application of polyhedra. After all, maths doesn’t get applied much when you’re in Grade 5.