Curving / Arcing stars

Hi all, I wondered if you could help me with a problem - I'm sure it's really simple but I can't figure out a way to do it.
Ihave a logo created by someone I work with, it looks great but it needs tidying up.  Now as you can see the outline is a 10 point star which has been curved, now I need to re-create this but make each point curved and exactly the same, so it mirrors itself. But I can't do it.
I can draw a star and use curced edges but that doesn't work - abnd I don'\t want to curve each point as they won't be identical.
Can anyone solve this little puzzle for me?
Thanks loads in advance,
Dave

Draw one side of one point, curved as you want it but a bit longer on the inside than it needs to be.
Reflect-copy it and join the ends to make one whole symmetrical point.
Give it a fill colour.
Mark the geometrical centre of your star (I often do this with 2 intersecting ruler guides).
With the Rotate tool rotate-copy your star point with the rotation origin on the intersection of the guides. For ten points this will be 36°.
Join everything up, probably using Pathfinder Unite, release compound path and Unite again.

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