An order of the cnidarian subclass Alcyonaria (Octocorallia) which lacks coenenchyme (the gelatinous layer, or mesoglea, surrounding and uniting the polyp). They form either simple (Cornularia) or rather complex colonies (Tubipora). The polyp has a cylindrical body with a retractile oral portion which can withdraw into a solid anthostele (the basal portion of the polyp) or calyx protected by many calcareous spicules. Cornularia, with a horny investment, lacks spicules. The base of the mature polyp is attached to a creeping stolon which is a ribbonlike network or thin flat mat from which daughter polyps arise. Daughter polyps never bud from the wall of the primary polyp. Each polyp is connected by solenial tubes of the stolons, or by transverse platforms as in Tubipora.