By George Hart for the Museum of Mathematics


The little metal connectors and plastic tubes that chemistry students sometimes use to make chemical models can also be used to make interesting geometric models. Here is a 50 inch diameter Goldberg polyhedron made from 420 three-way connectors and 630 plastic tubes (of two different lengths). Here are more photos and instructions for making your own version.

There are 12 pentagons and 200 hexagons. This is called the (4,1) Goldberg polyhedron because if you start on any of the 12 pentagons, face outward in any of the five directions, and take four steps in a row on hexagons and one step to the left, you will end up on another pentagon.

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.

  • Cypher Porter

    I can’t find information on the type of model kit anywhere in the links of this article. It doesn’t seem to be that common of a kit for chemistry modeling, at least according to google and amazon. Any hints?

  • Hannah

    It looks like an inorganic modeling kit–they use these more often when going over crystal lattices and macro structures that benefit from the flexible tubing approach. I’m not 100% on the manufacturer for the parts in particular kit, but try this site for options: