Studies in Sphere Packing

by Kirby Urner

First posted: Feb 12, 2002
Last Modified: Feb 26, 2002

Fig 1: SIAM company Java applet (try it!, you'll like it!)

Essential to figuring the convex hulls, given a set of vertices, was Qhull, freely available geometry software designed for this purpose. The glue language for linking raw data from the SIAM applet, to Qhull, and to Povray and VRML as output options, was Python (LiveGraphics3D and EIG formats also in the works).

Fig 2: The nuclear ball (Ball #1) surrounded by its Voronoi cell.

This is the nuclear ball in a 1000-ball packing returned by the Java applet above. Note that it looks very much like a regular pentagonal dodecahedron, although it isn't, quite (check the VRML view for a better sense of it).

Fig 3: Nuclear sphere (Ball #1, green)
with 3 touching neighbors

Fig 4: Ball #11 (green) with 3 touching neighbors.


The voronoi cell around Ball #11 has 13 facets, while its neighbors have 13, 14 and 15 facets.

Ball #11 has 10 touching neighbors. These, and 3 more nearby spheres will all share a facet of its voronoi cell.

Additional Resources:

oregon.gif - 8.3 K
Oregon Curriculum Network