# Automorphism

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In mathematics, an **automorphism** represents any of the inner symmetries of a mathematical structure. Formally, it is defined as an isomorphism from an object to itself. Examples relevant to polytopes include automorphisms of abstract polytopes, automorphisms of groups, and automorphisms of fields (to define conjugates, for instance).

All of the automorphisms of an object form a group called the automorphism group. This essentially generalizes the symmetry group of geometric objects to more abstract concepts.

For the specific definitions for polytopes and groups, see the corresponding sections of the isomorphism article.

## External links[edit | edit source]

- Weisstein, Eric W. "Automorphism" at MathWorld.
- Wikipedia contributors. "Automorphism".