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That looks like a Goniopora to me. They are supposed to be pretty difficult to care for. If they get even the smallest injury the whole thing will likely die.
+1 on the GSP
My green star polyp did that for about two weeks as I tried everything I could to get it to open back up. What worked for me was running carbon for a while and it opened back up in a day or two. From what I've heard they are sensitive to certain chems in the water and the carbon will remove them. Make sure your water is good and post your params. Good luck!