This next coral comes from the Lousiville Limestone near Louisville, KY. It was found at a site of mixed eroded material from both the aforementioned formation and the Jeffersonville Limestone. It's a small coral with a distinct looking calice that is flat near the edge but very straight and deep.
I used the book by Erwin Charles Stumm; "Silurian and Devonian Corals of the Falls of the Ohio". to help ID and found a possible match with Tryplasma prava on page 51, plate 6, fig. 1, 3, 7-8. In his description Stumm says "Exterior typically very closely annulated with superposed former (calice) margins 0.5-3mm apart." and "(Calice) walls steeply sloping to vertical with shallowly inwardly sloping margin in some specimens."
Those descriptions match this specimen very well as it does have what appear to be multiple calice growths (perhaps a sign of rejuvenation or just the growth habit of the coral) as well as having steep walls in the calice itself.
This and the next two pictures are the sides of the specimen as seen rotated 120 degrees from the prior picture.
A view of the calice at an angle to show the steep walls.
Top view of the calice showing how the walls are straight to slightly sloping inward.
I believe this specimen comes from the Lousiville Limestone near Louisville, KY and is dated to the Silurian period (Homerian to Gorstian stage).
References: Stumm, E. C. (1964). Silurian and Devonian corals of the falls of the Ohio. New York: Geological Society of America.