Polished Orthoceras Fossil in Matrix - Small Archeology Specimen The study of complex creatures that inhabited the Earth millions of years ago takes us to the orthoceras (straight horn). It is a genus of extinct nautiloid cephalopod. Orthoceras fossils are common and have a global distribution, occuring in any marine rock, especially limestones. Orthoceras are slender, elongate shells with the middle of the body constricted, and a subcentral orthochoanitci siphuncle. The surface is ornamented by a network of fine lirae.