Unsurprisingly, several people reached out to me to say HEY NEW PENTAGON AMY, DID YOU SEE? I love you. You know me well.
There are two kinds of people fascinated with the idea of finding shapes that can fill a two-dimensional plane: geometry professors, and quilters. What's weird, and sad, is that they aren't really talking to each other. I've corresponded with a few of them, and as far as I can tell, there are quite a few mathematicians who are working on these problems, but the number of quilters playing with the end results likely can be numbered on my fingers and toes.