This group includes the corals, sea anemones, and jellyfish. Fossils of soft-bodied organisms like jellyfish aren't common, and come only as impressions in fine sediment, but fossils of corals, with their massive calcite skeletons, are very common. Of course, corals are among the crowd of organisms that have formed gigantic reefs. The name Cnidaria comes from the term cnidae, the stinging cells (Have you ever been stung by a jellyfish, or know someone who has?).
Cnidarians have radial symmetry.
Both solitary and colonial corals are known as fossils (modern ones are colonial). Solitary corals consisted of a single animal living in its calcite skeleton, just as a sea anemone today is a single cnidarian animal, but anemones are soft-bodied, having lost the skeleton in their evolutionary history. Colonial corals live in a communal skeleton, with individual coral animals living amongst a crowd of up to hundreds of others.
You probably know that corals, sea anemones, and jellyfish are quite colorful:
Images Source: Wikipedia
But the fossil coral specimens you see below have lost that beautiful color, and appear the usual color for limestone, dull grayish. So, use your imagination to think about ancient reefs -- they were colorful too!
There are several distinctive Paleozoic coral groups. The rugose corals include both solitary and colonial forms. The solitary rugose corals are called horn corals, for obvious reasons:
And some of the colonial rugose corals of Paleozoic seas were massive, and formed extensive reefs:
Note the polygonal pattern of individual coral animal homes (makes you think of a wasp nest, which is a convergent invention, emphasizing how to pack in close). In each spot, there are faint lines (you can't see in this photo) showing the familiar radial pattern of the individual animal's body. Now, remember -- use your imagination to plop in a colorful sea anemone-type coral animal in each of those spots.
Here's another Paleozoic coral, to show an example of the diversity of form:
You can see the radial pattern in the individual coral homes in this specimen.
And here is a modern coral, this particular species having a more densely packed arrangement of coral animals:
If we zoom in, we see the radial pattern clearly:
Its no wonder, after looking at the massive structure of these calcite skeletons, that when we hear coral, we usually think reef! This is true, going back to the origin of the entire group in the Cambrian.