Individual coral polyps within a colony are connected by common tissue.
Octocorallians have an internal skeleton. Some internal skeletons contain calcareous spicules. Spicules are either scattered of fused. They stiffen and protect the polyps. Other octocorallians have internal skeletons made of protein.
Reef-building corals secrete an external skeletal cup of calcium carbonate. This skeletal cup protects the polyp: when the polyp contracts, it's almost completely inside the skeletal cup. The stomach cavity of reef-building corals also contains radiating calcareous walls. These walls extend up form the polyp's base and reinforce the skeleton.
The mouth leads into the stomach cavity.
The stomach cavity is partitioned by longitudinal membranes called mesenteries. Mesenteries increase the surface area of the stomach cavity, which aids in digestion. The edges of the mesenteries in reef-building corals support long mobile filaments. These mesentery filaments can protrude through the mouth to capture food. Mesenteries also contain the reproductive cells.
Respiration (gas exchange) takes place through the body surface.