Hesperorthis, extinct genus of brachiopods, or lamp shells, which as fossils are especially characteristic of Ordovician marine rocks (438 to 505 million years old). The plano-convex shell of Hesperorthis consists of two units (or valves), the brachial valve being flat and the pedicle valve convex. The shell has a radiating pattern of ribs and a relatively broad, triangular area at the dorsal shell margin.