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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!

http://pubs.acs.org/doi/abs/10.1021/jp206115p

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    $\begingroup$ 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! $\endgroup$
    – mike van der naald
    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. $\endgroup$
    – mike van der naald
    Commented Jul 12, 2016 at 4:07

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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.

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    $\begingroup$ 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. $\endgroup$
    – Geoff Hutchison
    Commented Sep 15, 2015 at 19:54

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