I am assuming “Attack on the pentagon” is there as clickbait.
Fooled me five times. Shame on me.
Fooled me as well. Pretty clever though.
Sigh, it’s the third time I see the story, and all anyone talks about is the title.
I still can’t figure out the group of symmetries of this wallpaper pattern, though. And it’s frustrating that they haven’t published a paper either.
I think I’m not alone in passing over the article at first because it sounded like a bunch of nonsense.
No, it’s genuinely interesting. The crystallographic restriction is one of my favourite theorems. No 5-fold symmetry allowed! None above 6-fold either? Why? Because math, because pure thought. Physical reality has nothing to do with it. There’s no way this truth cannot be an everlasting truth. Sorry, 5 is just out of the question.
Only 17 wallpaper groups possible! This theorem is cool mostly because it points to more of the mystical properties of 17.
Artin Jr’s algebra book has a pretty good introduction to some of the basics of 2-dimensional crystallography.
To be clear, I liked the article once I read it. But “attack on the pentagon” set my expectations for some “water is wet” article.
It’s so beautiful! I mean really fascinating to look at and aesthetically pleasing. All of them! (there’s an image of all 15 known tiling pentagons at the end of the post). I’ve just been staring at them, and I keep going back.
My mind wants to see the pattern aligning to a rectangular or triangular grid, and they feel like they do, but then don’t. Yet they are totally regular. And so pleasing.
Before this, I never considered that pentagons could tile at all. Wild.
This is cool and all, but I read the title as “Attack on the Pentagon results in discovery of new mathematical life” and can’t help but be disappointed.