Rounded Corner Effect using Divide effect
Step #1: Draw a star
Draw a star with the Star Tool. Copy it by pressing Ctrl+C/Command+C to the clipboard.
Step #2: Creating rounded corner effects
Go to Effect>Stylize>Round Corners. Enter a value for the Radius. Check the preview to get the amount of rounded effect. For expanding the shape, use Object>Expand Appearance.
Step #3: Divide the corners
Paste the sharp corner star to the front by pressing Ctrl/Command+F. Choose both shapes and select Divide in the Pathfinder palette(Window>Pathfinder).
Step #4: Delete unwanted corners
Using Direct Selection Tool, choose the unwanted corners and delete it to get the final honey star shape.
We can use this method on any shape to achieve the combination of sharp and rounded corners using the Rounded Corners effect. As you applied the Divide command the shape will break into pieces. You can combine the shape by selecting all the broken shapes and apply Merge command in the Pathfinder.