The hat tiling is 2D. There are some 2D crystals like graphene, but those are interesting because they actually exist.

A decade ago I would have agreed with you. But then I discovered the topic of five-symmetries and my absolute favorite non-toxic non-stick pans are coated with that alloy (not long ago deemed impossible) that has the five way symmetry.

So the practical applications are not far behind for these "only 2D" crystals.

Looks like you're referring to https://en.wikipedia.org/wiki/Quasicrystal#Applications, marketed as Cybernox.

But 5 to 13 is a huge jump.

https://www.technologyreview.com/2011/10/12/190784/the-quasi... says "They closed the production line because they had a few problems in the reaction of the coating with salt. If people cook with a lot of salt it will etch the quasicrystalline coating. People didn’t like it, so they did not continue."

I see comments about Cybernox from 2001, so the patents might've expired by now.

Many bits of physics start out as "did geometry". Will this particular idea pan out? Probably not. Should it be the subject of popular press at this stage? Probably not. But it's worth having scientists explore the possibilities. The paper might be interesting to specialists, once published, https://journals.aps.org/prl/accepted/33074Yb3Ufa1478fd33b04...

Quasicrystals is an excellent example. Penrose tiles were invented in 1974, but quasicrystals were discovered in 1982.

It's, in practice, applied gradient-based optimization on a geometrically-defined objective, which means if you squint hard enough it's machine learning.

(I am a crystallographer turned machine learning engineer.)