  Orbit spaces of the reflection representation of finite irreducible Coxeter
groups provide polynomial Frobenius manifolds. Flat coordinates of the
Frobenius metric $\eta$ are Saito polynomials which are distinguished basic
invariants of the Coxeter group.
  Algebraic Frobenius manifolds are typically related to quasi-Coxeter
conjugacy classes in finite Coxeter groups. We find explicit relations between
flat coordinates of the Frobenius metric $\eta$ and flat coordinates of the
intersection form $g$ for most known examples of algebraic Frobenius manifolds
up to dimension 4. In all the cases, flat coordinates of the metric $\eta$
appear to be algebraic functions on the orbit space of the Coxeter group.
