I’ve been trying to figure out the exact shape of the iOS 7 icons, with the help of Manfred Schwind and Michael Flarup. I initially thought it was a perfect superellipse, but that turned out to be incorrect (it’s close, but not close enough).
Manfred’s solution of grabbing the path data from iOS has proven to be the closest, but it’s still not absolutely perfect, as can be seen from the image diff above on the right. This may be down to differences in antialiasing. Please note that I compared Safari’s SVG rendering (which I assume is the closest to, or matches CoreGraphic’s shape rendering) and Photoshop’s shape rendering — the final icon shape AA was closer using Photoshop's shape AA (image diff, with Safari on the left and Photoshop on the right).
Further reading:
Exploring iOS 7 Rounded Corners
Start making iOS 7 Icons with the App Icon Template 3.0