Densest Packing of Spheres in a Sphere

Last update Aug 25, 2013

This Applet needs a Java Plugin (tested:1.4, 1.5.0_06).

Enter a number from 1 to 72 in the text field and press "apply" or hit [ENTER]. You will see the first sphere of the packing (parallel projection). Then you can put next spheres with "(+)", remove last with "(-)" or all with "all". In the select box you can change the point of view. Attention, the spheres will come in a different order (from back to front). Selecting "touches" shows lines if a sphere is in touch with another sphere.

If symmetries are available you can select it. Show different symmetry operations with the "0" Button. Gray color means the ball is translated onto itself. Spheres of other colors are translated (e.g mirrored or turned) onto another sphere of the same color.

You can also rotate by mouse drag, or by typing [x],[y],[z] on your keybord. [+] and [-] zooms in or out. You can also use the arrow keys. [ctrl] is finer, [shift] changes direction. Click on the spheres first to assign the input focus.

The comprehensive update of data in August 2013 includes the results provided in a private communication by Liang Yu. Prepared for visualization by Hugo Pfoertner.
Mathematical questions please to him. (For all packings with n>12 there are no proofs of optimality)

For critics, suggestions, etc. about the applet mail to martin . erren @ gmx . de (without spaces).

Links to the data: Coordinates, symmetry groups and radii of best known solutions up to n=72.

See also Densest Packing of Spheres in a Cube.

Have fun!