The hat tiling is 2D. There are some 2D crystals like graphene, but those are interesting because they actually exist.
So the practical applications are not far behind for these "only 2D" crystals.
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.