This weekend a couple of my daughters and I put together a buckyball from a Zometool kit. The shape is named for Buckminster Fuller of geodesic dome fame. Two years after Fuller’s death, scientists discovered that the shape appears naturally in the form of a C60 molecule, named Buckminsterfullerene in his honor. In geometric lingo, the shape is a truncated icosahedron. It’s also the shape of many soccer balls.
I used the buckyball to introduce the Euler’s formula: V – E + F = 2. (The number of vertices (black balls) minus the number of edges (blue sticks) plus the number of faces (in this case, pentagons and hexagons) always equals 2 for a shape that can be deformed into a sphere.) Being able to physically add and remove vertices or nodes makes the induction proof of Euler’s formula really tangible. Then we looked at 6- and 12-sided dice to show that V – E + F = 2 for these shapes as well.
Thanks to Zometool for sending me the kit.
Related post: Platonic solids