Mark Stanton writes on Apple's corner design:
...you might look at Apple’s icons and think that they’re just a rounded square or a ‘roundrect’. If you’ve been designing icons, you know that they’re something different and may have heard the word squircle used (mathematical intermediate of a square and a circle). And if you’re an Industrial Designer, you recognize this as a core signature of their hardware products.Ever since iOS 7, app icons went from being rounded squares to something more complex and refined. While everyone gets that Apple pays attention to the most minute details, not everyone sees the obvious logic behind this seemingly small change.