Part of my research is investigating sphere packings and their properties.I really would like a large database of sphere packings that I could investigate using a program I have written that tells me certain things about the packings. After doing some research I found some online databases but a lot of them haven't been taken care of so they're riddled with dead links. I was wondering if anyone knows of any books or websites that have a lot of sphere packings that I could investigate. Or if there is a way to interpret crystal structures as a sphere packing, seeing how there is a lot of crystal structure databases.

If anyone is confused as to what kind of data I'm looking I just need coordinates of the centers of spheres and their corresponding radii. These need to form a packing where the spheres are touching like in this paper where the authors have found new bi-disperse packings. Thanks!


  • $\begingroup$ there are several open crystallographic databases with various liberty of access, but selecting and extracting sphere packings would be up to programmer. $\endgroup$
    – permeakra
    Commented Jul 12, 2015 at 8:19
  • $\begingroup$ That is exactly what I would like to do, permeakra! I guess I'm unsure as to how I would take one of these databases like, ccdc.cam.ac.uk/pages/Home.aspx or webmineral.com and begin extracting sphere packings? Sorry for the late response I should have checked this sooner, thank you for your reply! $\endgroup$ Commented Jul 14, 2015 at 17:09
  • $\begingroup$ It is not clear what you want to do. Molecules are not spheres, so only crystallography database I would call "spherepacking" would be crystals of metals and simple salts. Of course, it is arguable how far they are spherical, too. $\endgroup$
    – Greg
    Commented Jul 12, 2016 at 4:00
  • $\begingroup$ I think it's very clear from the post what I want to do, I want a database of sphere packings. Nowhere in my post do I say that molecules are spheres or insinuate that. Perhaps you meant to put this on my answer? Either way, it's straight forward to interpret crystallography data as a sphere packing. Take the Cartesian positions of the atoms and then take those positions for the center of spheres. $\endgroup$ Commented Jul 12, 2016 at 4:07

1 Answer 1


I have found a partial answer to finding a large database of sphere packings, thanks to the comment from permeakra!

So far I have been obtaining .cif files from the large databases of crystal structures online such as, http://www.crystallography.net/. Once I have the .cif files I use openbabel to convert those files to .xyz files. From here I have a table that describes a crystal's structure by the x,y, and z coordinates of each particular element for example,

\begin{array}{c|c c c} \ce{Mg} & 1.01054 & 1.01054 & 1.01054\\\hline \ce{Al} & 1.01054 & 1.01054 & 1.01054\\\hline \ce{Al} & 4.04217 & 4.04217 & 4.04217\\\hline \ce{Mg} & 4.04217 & 4.04217 & 4.04217\\\hline \ce{O} & 2.11390 & 2.11390 & 2.11390 \end{array}

But my problem from here is that babel has failed to return the ionic radius which I suppose can be retrieved online via wikipedia or something. I posted another question that is more specific to .cif files which expands on this problem which can be found here, Extracting "Crystal Radii" from a CIF file.\

Limitations to this approach include that I can only find 3D sphere packings and it's a rather long and clunky procedure for obtaining lots of sphere packings.

  • 1
    $\begingroup$ It's not clear to me what kind of radius you want - certainly Open Babel has van der Waals and covalent radii as I indicated in the other question. $\endgroup$ Commented Sep 15, 2015 at 19:54

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.