  It is known that the orbit spaces of the finite Coxeter groups and the
Shephard groups admit two types of Saito structures without metric. One is the
underlying structures of the Frobenius structures constructed by Saito and
Dubrovin. The other is the natural Saito constructed by Kato-Mano-Sekiguchi and
by Arsie-Lorenzoni. We study the relationship between these two Saito
structures from the viewpoint of almost duality.
