'automorph' originates from Greek, specifically the elements 'auto-' and 'morphē', where 'auto-' meant 'self' and 'morphē' meant 'form' or 'shape'.

'automorph' was formed in modern scientific/technical English from classical Greek elements (compare Greek 'αὐτό-' + 'μορφή' / 'automorphē') and is related to terms like 'automorphism' formed via Medieval/Modern Latin/Greek technical coinage.

Initially formed from components meaning 'self' + 'form'; over time it has been used in technical contexts to denote a map or transformation that preserves structure and maps an object to itself, essentially becoming synonymous with 'automorphism'.