Class of animals that were usually solitary, only rarely colonial, found in Lower and Middle Cambrian deposits. The conical cup varies from cylindrical to saucer-shaped, and usually consists of two porous walls (a single porous wall in the order Monocyathida). The intervallum may contain tabulae alone or with septa. There is a fan-like divergence of longitudinal pore-rows in the septa. Dissepiments may be present. Some single-walled monocyathids had a flap (pelta) over the central cavity. Compare irregulares.