No "coral expert" here, but I have seen several different types of solitary
corals, both fossil and recent.  Both types can be purchased quite
inexpensively, so they must be pretty common, both now and in times past.
Some types are rather heavy and solid, with conical bases, and lie on their
side on the sediment.  But the ones I like best are the delicate forms that
have long, slender, leg-like projections that support the polyp upright on
the sea bottom.  Some of them are quite pretty.  The polyps of solitary
corals are generally much larger than those of colonial corals, sometimes as
much as 10 cm or more in diameter, resembling sea anemones.
Paul M.