Math Monday: Fractal Polyhedral Clusters
JANUARY 4, 2010

by George Hart

At the Math Museum, we are interested in making cool mathematical ideas accessible and tactile. With a good 3D printing machine, you can make beautiful fractal polyhedral clusters like this. The nylon model above consists of twelve groups of twelve small stellated dodecahedra. Each group is arranged like an icosahedron and the whole is an icosahedron of icosahedra.
Polyhedral Cluster Animation
It is beautiful to turn this in your hand and see its patterns and structures from all angles. If you have access to a 3D printer and want to make your own copy, you can download the stl file from here.
Twelve Great Icosahedra
This delicate pink sculpture illustrates the structure of just one subcluster from the above, but here each element is a great icosahedron, where above the elements are small dodecahedra.

This article first appeared on Make: Online, January 4, 2010.

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