  Mirror graphs were introduced by Bre\v{s}ar et al. in 2004 as an intriguing
class of graphs: vertex-transitive, isometrically embeddable into hypercubes,
having a strong connection with regular maps and polytope structure. In this
article we settle the structure of mirror graphs by characterizing them as
precisely the Cayley graphs of the finite Coxeter groups or equivalently the
tope graphs of reflection arrangements - well understood and classified
structures. We provide a polynomial algorithm for their recognition.
