By George Hart for the Museum of Mathematics


Pipe cleaners are easily woven into flat lattice patterns, but spherical weaves are more challenging. Here is a good exercise in spherical thinking that is much harder than it looks. The thirty pipe cleaners each have the same shape and the same relationship to their neighbors.

The pattern is indicated in the diagram below, where the black triangles correspond to the faces of an unfolded icosahedron and the red curves are the paths of the pipe cleaners. If you cut out twenty of these triangles and tape them together to make an icosahedron, you’ll have a template for the weave.

Detailed instructions for making your own spherical patterns are online here.

See all of George Hart’s Math Monday columns