As far as the math is concerned... What I'm actually working on is a methodology for identifying possibly interesting classes of polygons, finding interesting things about those classes, and establishing connections between different classes. That stuff would be extremely hard to explain to non-mathematicians. (I tried to do so, once, on DW, but didn't get very far.)

But there's another layer to it: the results of applying that methodology. That is, I could describe some of the classes I've discovered and say what's interesting about them. That, or at least some of that, might be more accessible. I might give that a go sometime soon.