It's flagstone. Many people have success with it. Many do not. I'm one that didn't. I believe it has to do with which quarry it comes from. The problem is that flagstone, like all sandstones, consists of layers of compressed sand. Water is not kind to that geological make up. It can break down and become sandy and/or come apart in flakes, large and small. I've had all of those problems.
There is a very expensive chemical process that can be applied to keep most of it from happening, and that process (about $3K for my small-ish pool) has helped quite a bit, but not 100% solved.
Also, I was first very concerned about the jagged nature of the edge (which admittedly is one of the things I like best about it). So far none of the kids has been injured by it, but it has some potential to leave a nasty "road rash" if hit just so. Other types of coping have different degrees of this possible problem, but flagstone is probably among the worst of them.
So yes, I think it's gorgeous, too. But it can have issues...