ROLL THE TIPS
The lily variety has four tips. To breathe life back into it, you must roll said tips (individually) around the barrel of a pen. A classic Bic Roundstic is the correct diameter that delivers the proper effect. This embedded video demonstrates what I am talking about. It's very simple.
The key is to ensure that you get each pointy tip to CATCH under the pen on the first rotation. This ensures that as you roll all of the way down, tension will be created in the petal, thus ensuring the curve in the paper holds. Do not be afraid to peel / roll each tip all the way down as far as it will go. Remember to keep the paper TAUGHT as it wraps itself around the barrel of the pen. Good luck!