  We consider the polynomial representation S(V*) of the rational Cherednik
algebra H_c(W) associated to a finite Coxeter group W at constant parameter c.
We show that for any degree d of W and nonnegative integer m the space S(V*)
contains a single copy of the reflection representation V of W spanned by the
homogeneous singular polynomials of degree d-1+hm, where h is the Coxeter
number of W; these polynomials generate an H_c(W) submodule with the parameter
c=(d-1)/h+m. We express these singular polynomials through the Saito
polynomials that are flat coordinates of the Saito metric on the orbit space
V/W. We also show that this exhausts all the singular polynomials in the
isotypic component of the reflection representation V for any constant
parameter c.
