I’ve been reading up on crystallography recently for an upcoming project, and I was having a hard time wrapping my head around Miller indices. I kinda got it, but I wanted something tangible to work with, darn it.

I started making 3D models in CAD, and also cutting up pieces of wood to glue together, when I realised that I already had a prototyping system in my living room that would be perfect for the job.

Lego. Is any engineer’s bookcase really complete without it? 

It’s perfect for displaying the various crystal faces.

Lego with a Miller Index of (1,0,1)

And you can see how the ratios of unit cells in X,Y,Z lead to different angles on the face:

Playing around with these models gives one an extremely clear demonstration of the reason behind Steno’s Law (That angles between corresponding faces on crystals are equal for all crystals of the same material). In this metaphor “same material” translates to “same size unit cell” same size lego brick.

And of course the standard 100, 010, and 001 faces. In this case they’re at right angles to each other, but that’s only because the (lego) unit cell is orthogonal. It’s perfectly possible to find crystals where 100 and 010 faces are at angles other than 90 degrees. 

So, I’m now happy I understand the basics of the Miller Indices, but much like Mary Poppins, lego can’t stay still in one place forever. I decided to make a more permanent set of faces to have on hand so I could free up my lego again.

Here’s some I made from balsa bricks:

The unit cell here is anything but cubic, which I’m actually quite pleased with. It shows how crystals aren’t just a collection of perfect platonic solids. 

And a few years ago I did a large bulk purchase of cedar cubes and spheres (I had a rough idea of making a marble computer), and I decided to put them to good use: 

I attempted to try and cram in the most informative faces for a fixed number of cubes by fitting in the (0,~2,1) and (0,1,1) face as well.