  In these notes we investigate the rings of real polynomials in four
variables, which are invariant under the action of the reflectiongroups [3,4,3]
and [3,3,5]. It is well known that they are rationally generated in degree
2,6,8,12 and 2,12,20,30. We give a different proof of this fact by giving
explicit equations for the generating polynomials.
