Common Name is Fire Coral, Lace Coral, and Stinging Coral
When I was in Belize, they warned us not to touch them because they have toxins that will cause a painful chemical burn on the skin.
Besides this, hydrocorals are reef building corals but are different than other SPS corals because their polyps are within the coral.
There are different types of hydrocorals, some of them are branching, some encrust, and some plate. They can also encrust other living corals.
They are found worldwide. Live in areas of high water flow and live between sea level to 130 ft. deep. They are one of the first corals to colonize reefs and one of the last types of corals to die on a reef, they are very adaptive. They are photosynthetic and are usually yellow in color.
From Eric Borneman's "Aquarium Corals"
IMO the best book I have read on corals. Very informative and a must for someone who really wants to understand what it takes to keep coral alive and thriving.
Hope this helps.