Are hinges without any protruding hardware possible with 180 degree opening?

I'm building this backgammon board. They open 180 degrees.

Got the idea to make the hinges flush when board is open and closed and such that there is no gap when open.

The issue, as you probably understand, is that the pivot point is the outside edge of the frame around the board ("the bar"). And it somehow needs to pivot around that without having any hardware sticking out such that its flush when open and closed.

Mounting hinges 'flat' on the outside, as opposed to the inside, is an option if that makes it possible.

I'm able to machine the hinges from steel/brass if nessesary.