'axisymmetric' is formed in English by combining 'axis' (originating in Latin from the word 'axis', ultimately from Greek 'áxis' meaning 'axle' or 'pivot') and 'symmetric' (originating from Greek 'symmetria', where the prefix 'sym-' meant 'together' and 'metria' meant 'measure').

'axis' came into English via Latin 'axis' (from Greek 'áxis'), and 'symmetric' comes from Greek 'symmetria' via Late Latin/Old French; the compound 'axisymmetric' arose in technical English (20th century) by joining 'axis' + 'symmetric' to denote symmetry about an axis.

Initially the components referred separately to an 'axis' and to 'symmetry'; over time the compound came to specifically mean 'invariance under rotation about a given axis' in scientific and engineering contexts.