Ball-and-Stick Quasicrystal Model

[person123]

TL;DR Summary

I'm looking to 3D print a ball-and-stick model (think organic chemistry kit) of a quasicrystal, and I'm looking for some guidance.

I'm imagining something like this:

The image was taken from the following paper, and is described as a rhombicuboctahedral quasicrystal. The paper itself gets very technical (at least for me), describing projecting a 4D crystal into 3D space. It seems to me based off of a rhombicuboctahedron, although I don't know if it's correct to naively use the angles from that shape when creating a ball and stick model.

I'm not fixed on this particular type of quasicrystal; any aperiodic 3D structure would do. (The more aperiodic, or more specifically the fewer continuous open channels, the batter).

My main question is, for whatever quasicrystal I choose: how do I determine what the orientation of the balls in the holes should be?

I'm also curious how easy it would be to assemble. If my memory serves me well, when using Penrose tiles, it would always be possible to fit another piece in when tessellating with them -- you would (at least in general) never get stuck. Would something similar occur for a ball-and-stick quasicrystal?

There is a video of someone designing and printing a quasicrystal assembly, so I have some confidence this is doable, but this is very new to me, so any guidance would be very helpful.

Thanks!

 

[jedishrfu]

First for other readers of this threads there are two distinct quasi crystal usages:

quasicrystal

vs

quasi-crystal

This thread discusses the first one, the quasicrystal.

I found this wiki article on it with a stick diagram of an icosahedral crystal diagram that may be what you are looking for.

https://en.wikipedia.org/wiki/Quasicrystal

 

[person123]

This is the image:

I'm still not sure how to figure out the orientation the holes in the balls would have to be though.

 

[berkeman]

I'm still not sure how to figure out the orientation the holes in the balls would have to be though.

Wait, I thought you wanted to 3-D print this, but are you saying you are just going to 3-D print the sticks and the balls with holes in them to connect the balls with the sticks as you assemble this? I guess I misunderstood your original question...

 

[person123]

Sorry for the confusion. Yes, I want to just 3D print the balls and sticks, allowing a person to assemble it.

 

[berkeman]

Well, you will need the 3-D positions of each of the balls in the figure you want to make. If you have that data and know which balls need to connect to each other, the math isn't too bad to figure out the 3-D angles. The harder part is finding the 3-D position data for the figure you want to build. Can you find such data in the references of the Wikipedia article for one of the figures you want to build?

 

[person123]

I can't find the data in references or other articles. I was able to find a CSV file from the video on the quasicrystal model. However, when I tried plotting the points (which I thought represented vertices), I got the following (blue is $(x_1,y_1,z_1)$ and red is $(x_2,y_2,z_2)$):

This is what the actual model looks like:

Clearly I'm misunderstanding what the data in the file is representing.

 

[Baluncore]

Check the file format, maybe that file gives the connecting sticks as lines.
Line from x1, y1, z1 to x2, y2, z2; gives the ends of every line in 3D.
Look for duplicate x, y, z values to identify the position of atoms.
Zoom in close to see fine detail.

 

[person123]

That's what I thought, but the distance between the points ($\sqrt{(x_4-x_1)^2+(x_5-x_2)^2+(x_6-x_3)^2}$ for each row), ranged from 0.2 to 17, and it seems to me that the distances between points are the same based on the model.

I could make an issue in the Github, but I feel like I must just be missing something obvious.

 

[Baluncore]

Google ' quasicrystal csv '
The first result is; https://arxiv.org/ftp/arxiv/papers/1805/1805.11457.pdf

 

[Baluncore]

If the data is a bonding table of atoms then there is only one type of atom present.
There are 3924 atoms in different positions.
Counting the references to each gives us the number of bonds.
It seems like there is something wrong with the data table.

Bonds, Atoms
1, 1117; These 1117 atoms connect to only one other, so are probably at the edges.
2, 890
3, 511
4, 413
5, 256
6, 204; These have 6 contacts.
7, 126
8, 114
9, 52
10, 49
11, 44
12, 49
13, 34
14, 12
15, 15
16, 8
17, 9
18, 5
19, 5
20, 2
21, 1
22, 4
23, 2
31, 2; Only two atoms have 31 bonds.
total 3924 atoms

 

[person123]

An image in that paper of this quasicrystal sculpture piqued my interest because the nodes seemed to be simply dodecahedrons:

I found a (sort of) paper by its creator confirming it is indeed just dodecahedrons.

Determining the orientation of the holes for a dodecahedron, whether by using the CSV file, searching it up, or with pencil and paper, shouldn't be much of a challenge.

I'm not sure if it's really that simple though (at least for this quasicrystal). It seems to just be dodecahedral nodes and rods of constant length. Is there anything I'm missing?