Not much is known about the Polygon's history, except that when Cyrus and Antigone first go there the only inhabitant are Nolan (who lives in a crypt inside of the Polygon) and many deadly whip spiders.
In The Dragon's Tooth, the Polygon is described like this:
The room is sprawling, the ceiling is low and pocked with vaults. Squat columns are scattered throughout the room and all the stone is painted white. Lots of the paint is peeling. The floor is dusty white linoleum and white triple bunks are against the walls. There are lots of walls. There are exercise posters on a bunch of the walls and Nolan set up planks all throughout the room to walk on. He also oiled the walls and ceiling to protect himself from the whip spiders.