WOOGLIN, Alan.
If you look at TBS site they list these corals...
Cladacora arbuscula tube coral
Phyllangia sp. cup coral
Siderastrea radians star coral
You have :
Cladacora arbuscula tube coral
Siderastrea radians star coral
in your photo, the colony in the middle is the CLADACORA ARBUSCULA, on the right bottom is SIDERASTREA RADIANS....
I have 130 pounds of rock with those corals and more... I have the same open brain you have, but haven't found a conclusive ID in the books I have, but I have for the corals you have, TBS is correct in their ID.
I can't image you don't have any PHYLLANGIA CUPs I have tons on my rock, they are like little black and white buttons with little clear polypys that extend, kind of like the cladacora, but different, longer polyps and not quite like the complete cirlcle of polyps extending from, but the single(tenticles) extending from the button...... they don't grow so much in colonies like the Cladacora... and sometimes they don't have any polyps extended, they just look like buttons.... I have found very little documentation on them, actually only on one state of texas website.
I hope that helps
Corey