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 or with the container.

If symmetries are available you can select one. Show the different symmetry operations with the "0" button. White (grayish shaded) means the ball is mapped onto itself. Spheres of other colors are mapped (e.g. mirrored or rotated) onto another sphere of the same color.

You can rotate by mouse drag (or finger drag on touch screens), or by typing x, y, z. + and - or the mouse wheel zoom in or out. You can also use the arrow keys. Ctrl is finer, Shift changes direction. Click on the picture first to give it the keyboard focus. "keep view" keeps rotation and zoom while spheres are added or removed; "link" (or key p) shows a URL that reproduces the current view.

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.)

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.

Original Java applet by Martin Erren; re-implemented in JavaScript (HTML5 canvas) in 2026 so that it runs in current browsers without Java.