by the way...........they do have mouths.
You wont see it until it opens fully.
When it opens fully you will see that it is sort of divided into two halfs. in between the halves is a line running down the middle of the entire coral, this is the mouth.
When you place food on the line, slowly (very slowly) it will open up and slowly surround the food and eat it.
It is amazing to watch eat!!!! I just have to keep the cleaner shrimp away from mine as he pulls the silversides right out of it's mouth. The coral is tooo nice. It refuses to sting the shrimp.