Fractal polyhedra clusters
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 polyhedra clusters like the one below. This nylon model consists of twelve groups of twelve small stellated dodecahedra. Each group is arranged like an icosahedron and the whole is an icosahedron of icosahedra.
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.
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.