But right now, all we have to "play with" is a window binary. I understand that there is supposed to be a paper published in the future; I would love to see this algorithm implemented into something more "universal", if nothing else.
Again, though, I can also see why such an algorithm could be protected - I am certain there are more than a few commercial applications for it, and perhaps in areas that have little to nothing to do with origami (for instance - and I am probably completely off base here - could this be applied in some manner to understanding protein folding?).
The main problem (apart from not modelling any of the chemistry of proteins) would be what your target shape would be. You can consider a folded protein to be the 'blob' formed by taking the surface formed by rolling a water across the outer atoms. Or you could consider just the backbone as a kind of tube.
An origami pattern for just the surface would have no internals. On the other hand, the pattern for the backbone would tell you nothing about how the sidechains and backbone interact.
Erik Demaine is a computer scientist: https://youtu.be/3e1ZF1L1VhY
I wrote print production (prepress) software. One of my inventions was an algorithm that converted book binding steps into impositions, as needed. (All previous solutions relied on catalogs of manually created "templates", for reuse, customization, etc.)
I'm now very curious if this general purpose origami algorithm can be used for the same purpose.
EDIT: teechap found it
Is this nation wide or only for my local area?
Jokes aside  the mathematics of paper folding is extremely interesting. The most interesting thing is that you can solve fourth degree equations with origami  .
 [ https://en.wikipedia.org/wiki/Robert_J._Lang ]
It would make a great book around computational art, rapid prototyping, kinematics, etc. The nice thing about origami is that it adds a physicality to mathematics that makes it tangible and approachable.
"Maybe links some of the triangles together" is the difficult part, especially since they guarantee the boundary of the paper folds to the boundary of the mesh.
From what I can tell, it appears that there are many locations where the original plane overlaps. If it is possible to easily calculate adjacency for those triangles, you would be able to properly do filtering lookups.
Another question is how much overlapping there is. The more there is, the more you potentially waste texture resolution.
Still, cool idea...
What about a lower(ish) tech solution involving say wood and mud? My aunt and uncle's previous house was largely that plus straw and (reed|straw) thatching and was originally built in the 1630's. It's not a particularly old example but one that springs to mind. We don't see many earthquakes, for example, here nor many forest fires but that house has stood through at least one or two 1 in say 300 year weather events - not least a bit of a cold spell in the 18th C and a few somewhat windy episodes.
That house has been patched up once or twice and I suspect that might be quite hard with your paper/card jobbie. The clearcoat will probably discolour badly and degrade within <10 years but obviously you could reapply it regularly. Swallows and House Martens or similar might also nick bits of it for their nests. I don't know what sort of insects you have to deal with where you are but they could also get nasty with a paper abode 8)
I suppose for disaster relief, cylindrical huts or igloo domes could be useful to minimize footprint, materials, and heating costs. But for permanent housing, most people will prefer vertical walls and right-angle corners.