The common name for four extinct classes of primitive echinoderms that have a flattened theca or body lacking radial symmetry. These enigmatic fossils were originally classified together in the class Carpoidea, but more recent echinoderm researchers have assigned them to four separate classes in the subphylum Homalozoa: the Stylophora (or Calcichordates), Homoiostelea, Homostelea, and Ctenocystoidea. These four classes include about 50 genera that range from the Early or Middle Cambrian to the Late Carboniferous.