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This specimen was observed on the beach in Russian Bay, Madagascar in the Nosy Be area. It was approximately 20cm in diameter and an inch thick at the tip of the "petals"..
I'm pretty sure this is an LPS, [= a Large Polyp Stony coral] ,a type of stony coral, order Sclerantinia, & in a 2002 expedition to madagascar, http://news.nationalgeographic.co.uk/news/2002/05/0515_020515_0515TVmadagascar.html (2 pages) a survey found it a very good place for corals with "a much larger coral diversity than expected" (with 9 new species according to Science Daily).
You're coral shows 4 features, turqoise outer rim, grey 'disc' ,red (& yellow) centre, & what looks like a purple plastic film on left hand side & around the bottom. There doesn't seem to be anything on the net to match the red centre,but it's presumaby the mouth, nor good matches for the rim or disc, but for the 'plastic film' http://yasminltf.blogspot.co.uk/2008/09/donut-and-modern-coral.html & http://www.reefcentral.com/forums/showthread.php?t=1241601 (4th pic) & http://species-identification.org/image_window.php?url=BIS/corals/pictures/trachyh4.jpg&title=Trachyphyllia
There's 1 site for Identifying the Reef Corals of the Indo-Malay Seas, http://species-identification.org/species.php?species_group=Corals&menuentry=inleiding ,with classification at http://species-identification.org/species.php?species_group=Corals&menuentry=groepen .NB it only goes down to genus level. In this classification It'd be in the Mussidae or Trachyphylliidae families (WoRMS, annoyingly, has a different classification).
The most likely of these seems Lobophyllia or Trachyphyllia or Symphyllia, & you can get the pictures by pressing [multimedia] eg http://species-identification.org/species.php?species_group=Corals&menuentry=groepen&id=101&tab=multimedia .
Examples showing diversity at http://www.ultimatereef.net/info/iddb/mussidae.php
While checking this I came across the coral expert Charlie Veron who explains here
http://coral.aims.gov.au/info/evolution-species.jsp that corals don't (as also plants I believe) conform to Darwinian evolution but rather to 'reticulate evolution'