I figured out the degree of freedom I forgot about. When you truncate, you can move new vertices in along old edges some amount, which you can choose. I split edges in three, moving each new vertex in by a third (see the diagram from wikipedia that I included in the previous post). Splitting in three makes sure you create regular hexagons for the soccer ball step (the truncated icosahedron). You don't have to create regular hexagons, and by modifying this you can make slim and broad rhombi, as shown in the images below.
This explains why I didn't match the values for the angles that I found on Wikipedia for the rhombic enneacontahedron. I suspect that most of these rhombic enneacontahedrons people make come from just a few instructional guides or paper folding guides online, which often refer to slim and broad rhombi, so probably they aren't making regular hexagons in the truncation step, which seems to yield very similar rhombi so that you can't easily call them broad or slim.
Extreme cases caused by changing parameter of truncation step seem to be less 'round'
Here's the final 3D printed assembly, after gluing in the magnets. The edge length on the edges the white and red tiles share are 2cm long, for reference
It would be fun to print the exaggerated versions with very broad and very slim rhombi at some point in the future.
Want to make your own? The code isn't super clean, so the steps at a high level:
- If you want to modify the truncation, you'll need to locate that section of the code, modify the appropriate line, and then get the code to spit out all the info you need on the angles and side lengths that are needed by the OpenSCAD script. There are a bunch of poorly commented areas where you can follow my pattern--I was working quickly and I just didn't make it easy to use yet. Sorry!
- If you keep the angles as in the OpenSCAD script, you'll make a shape like the one I made. You need to make sure the user controlled side length is the same for the tiles of type A and B. You also need to make sure you match the magnet info between those two types of tile.
- You can do this with just one magnet per edge if you want to save on magnets, though it won't be as strong and the tiles can pivot until locked into place by neighbors. You will need to go through my code because I didn't make it parametric either
Easiest way to do it? Keep everything exactly the same as my OpenSCAD code, render the STL and slice it for your 3D printer. Get at least 90*4 magnets, 3mm diameter by 2mm height, axially aligned. The magnet diameter and depth values in the script might still need to be adjusted to get a nice fit, depending on your 3D printer.