# Ice Crystal Matrix measurements of H2O molecules?

I want a mathematically generated 3D STL copy of this image, however it's represent algorithmically.

If I do all the H2O's as individual pieces with female connections prepared for chopped bike spokes, are all the H2O's the same and what angles do they have?

Is there a written array of positions and degrees of rotation of the water molecules of a regular ice matrix?

• crystallography.net/cod/1011023.html – andselisk Jan 18 '18 at 17:11
• – andselisk Jan 18 '18 at 20:03
• What do you need STL for? You won't be able to 3D-print that assembly of water molecules anyway. – andselisk Jan 18 '18 at 20:17
• I may print 3 atom H2O's molecules individually, including female sockets for bike spoke segments representing hydrogen polar links, then would the H2O's be all the same 3d model ? else i'd print it all as one using small links rather than bike spokes. – com.prehensible Jan 18 '18 at 21:16
• I have absolutely no experience with 3D printing, but I guess one can convert CIF file (first link) to XYZ format (e.g. with Mercury), then feed that XYZ to Blender, do fine tuning with 3D modeling there, and finally export to STL. If you really want to do it hard way, then all the necessary matrix operations are described by $P\mathrm{6_3cm}$ group itself so that the structure could be replicated. – andselisk Jan 18 '18 at 21:25

I decided to summarize all my comments in a form of answer and add some illustrations. Note that I have no experience in 3D printing, so I mainly focus on crystallographic part.

Since you asked for"a mathematically generated" 3D structure, you ought to know that water crystallizes in $P\mathrm{6_3cm}$ (# 185) space group having a hexagonal symmetry. Detailed information about symmetry generators and matrix transformations can be found online or in International Tables for Crystallography [1, pp. 582-583]:

There is already enough information to create a 3D model. If you want a more convenient way, you can get a CIF file for ice (COD-1011023) (which already embeds all the information above), and load it with Mercury (free, available on Windows, Linux, MacOS). From here on it's just a screencast of what's to click to get the desired molecular pattern like the one on your animated GIF:

1. Load the structure (drug-n-drop CIF file, or via Ctrl+O). What you see now is an asymmetric unit, in simple terms – a seed which an entire crystal structure can be grown from:

2. Let's expand the structure beyond those 6 atoms you've stuck with. Go to Calculate > Packing/Slicing.... Tick Pack option, and click + 0.5 boxes next to $a$ and $b$ axis:

3. Rotate the grown structure approximately like it's shown below:

4. Note that you have 4 water molecules on each side that you don't need. Those can be deleted by right-clicking on them and selecting Delete this molecule:

5. At this point you should have exactly the same 3D representation of the crystal structure:

6. Now you can print a 3D model directly from Mercury (File > Print in 3D...). The one with supporting framework looks like this:

6.1. Alternatively, you can save the structure as XYZ (Ctrl+S, choose Xmol files) and do some post-processing work in Blender if needed.

### Reference

1. International Tables for Crystallography: Space-group symmetry, 1st ed.; Hahn, T., Ed.; Fuess, H., Hahn, T., Wondratschek, H., Müller, U., Shmueli, U., Prince, E., Authier, A., Kopský, V., Litvin, D. B., Rossmann, M. G., et al., Series Eds.; International Union of Crystallography: Chester, England, 2006; Vol. A.
• very awesome information, i'll complete that and i'll have send an h20 ice kit in the comments. 3D printers are advancing nicely they are about 150 for smaller ones, it's a fun hobby. – com.prehensible Jan 19 '18 at 23:57

You can produce STL (and VRML) files directly from Mercury - see https://www.ccdc.cam.ac.uk/Community/blog/post-56/

I'm not sure how best you'd go about including female sockets for bike spoke segments, but be aware that for some 3D printing types you're charged for the total volume of material used, so you might be better off trying to create a model with multiple molecules in a smaller area with less empty space.

• Thanks, Mercury is very cool. I can't find a good ice file, I found a .cif file with 6 atoms only. How can I find ice/H2O from the cabridge/other databases? – com.prehensible Jan 19 '18 at 12:13