Complex Rounded Corners in Ai or Sketch

Question

I'm really inspired by Tim Van Damme's and Abstract's Mac Icon. The rounded corners that make up the icon are interesting to me. I've seen Tim make rounded edges like these before and would like to learn how it is done.

This is the icon I am referring too. In Ai or even Sketch, how would you approach or create rounded corners like this?

Image property of Abstract

Update:

I'm finding that image trace in illustrator to be somewhat helpful. It's not making this shape from scratch, but it is allowing me to study it better.

Answer 1

Any AI version

• Draw a circle
• Object > Path > Add Anchor Points
• Select the 4 original anchors on the circle
• Double-click the Scale Tool and enter a value less than 100%. Roughly 90-95% will provide those slightly rounded outer curves. The amount of the curve depends upon the percentage used.

Answer 2

In Ai:

• draw a circle
• take the direct selection tool
• move all 4 anchor points the same amount towards the center of the circle.

The following cartoon shows how to get exactly the same curvature as your model has. For different curvature have a differently sized square.

The final appearance need some coloring. Also some embossing is possible for metallic effect. Here's how to color:

Addendum - How I quessed the dimensions for an exact copy?

Maybe me, but no really creative artist think "that appearance needs a square with side length = the circle radius multiplied by the square root of 2" He needs a visual clue. This is the easiest exactly repeatable visual selection for the square size. I tested it and it happened to fit.