I was reading “On the order of the group of a planar map” (Journal of Combinatorial Theory, v1 #3 (1966) pp.394–395) about automorphisms of 3-connected planar graphs.
A rooting of a plane graph is a triple $(v,e,f)$; some root vertex $v$, an incident edge $e$ of $v$, the root edge, and $f$ a face incident with $e$, the root face.
The article says that it is easy to see that an automorphism of $G$ a 3-connected planar graph which fixes some given rooting must be the identity.
I miss the argument why this is true?