So, just thinking out loud, perhaps the rings in the chainmail above could be rings of carbon, just 6 atoms each. If so, would this be better than graphene at anything useful, or not? Would longer rings work better? The idea of carbon nanotube chainmail is about a decade old.
Powerpoint really is not designed as a proper drawing tool and not having a week to spare, I didn’t bother doing the link overlaps or even the bonds properly in my pic, but together with the other two, I think you will get the idea fine.
I don’t know if this will work or not, but it might be an idea worth looking at further.