By George Hart for the Museum of Mathematics


Here is a wide variety of mathematical beadwork structures by Horibe Kazunori.

Looking closely at one example, you can see how the surface curvature depends on the structure. Generally, six-sided cycles correspond to an infinite tessellation of hexagons, which makes a flat plane or can be rolled into a cylinder. But in the places where positive curvature (a spherical region) is desired, some pentagons are used instead of hexagons. And in places where negative curvature (a saddle-shaped region) is desired, some heptagons are used instead of hexagons. With this knowledge, the bead designer can control the surface outcome.

Horibe gives detailed instructions for making a beaded buckyball here. (It is in Japanese, but the pictures explain it all.)

See all of George Hart’s Math Monday columns

Gareth Branwyn

Gareth Branwyn

Gareth Branwyn is a freelance writer and the former Editorial Director of Maker Media. He is the author or editor of over a dozen books on technology, DIY, and geek culture. He is currently a contributor to Boing Boing, Wink Books, and Wink Fun. And he has a new best-of writing collection and “lazy person’s memoir,” called Borg Like Me.

  • Pan Dimensional

    Really clever, I’m going to try this :) (PS It’s a dodecahedron, not a buckyball – sorry, mathematician here :S )