This is from a 1 minute thought, so if it seems too easy and wrong, that is why. But i thought, wouldn't it turn into a circle? Or some "deformed" circle. The sides will keep going until they break and the corners just won't go too far, so you have 6 sides of "curveniess", thus your "deformed" circle. How to get the exact spacings? Trial and error. If it breaks, DUCT TAPE IT!!
Well, that is my very simple, and probaly wrong, answer...