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Apollonian Spheres

The Apollonian Spheres are a generalization to three dimensions of a beautiful construction with circles discovered by the ancient Greek mathematician Apollonius of Perga (late 3rd – early 2nd centuries BCE).
Like the Apollonian Circles, the Apollonian Spheres construction has fractal dimension, meaning its dimension is not a whole number. It is generated by an iterative process from a collection of starting spheres, in this case four spheres of equal radius contained in a fifth bounding sphere, with each pair of spheres touching at a point. The four spheres of equal radius sit with their centers at the vertices of a tetrahedron.
In our model, we have excluded the starting configuration of the outer bounding sphere and the four spheres of equal radius, in order to see inside the model.

Thanks to Prof. Rachel Maitra - WIT

Simon Williamson
Professor at Wentworth Institute of Technology Boston, MA