automorphism
/ˌɔːtə(ʊ)ˈmɔːfɪz(ə)m/noun
1 Mathematics. A transformation or correspondence that relates a set, space, etc., to itself; specifically an isomorphism of a structure with itself. Now rare.
2The attribution of one's own characteristics to another; an instance of this. Now rare.
Origin
Mid 19th century. From auto- + -morphism.