A systematic stereographic approach to the description of surface symmetry and structure, applied previously to face-centred cubic, body-centred cubic and hexagonal close-packed metals, is here extended to the surfaces of diamond-structure and zincblende-structure semiconductors. A variety of symmetry--structure combinations are categorised, and the chiral properties of certain cases emphasised. A general condition for non-polarity in the surfaces of zincblende materials is also noted.