Wilson operation

They are generated by two involutions on embeddings, surface duality and Petrie duality, and have the group structure of the symmetric group on three elements.

They are named for Stephen E. Wilson, who published them for regular maps in 1979;[1] they were extended to all cellular graph embeddings (embeddings all of whose faces are topological disks) by Lins (1982).

These operations are characterized algebraically as the only outer automorphisms of certain group-theoretic representations of embedded graphs.

[3] Via their action on dessins d'enfants, they can be used to study the absolute Galois group of the rational numbers.

-fold product of copies of the three-element symmetric group.