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.
More: See all of George Hart’s Math Monday columns