Kato، نويسنده , , Mitsuo and Sekiguchi، نويسنده , , Jiro، نويسنده ,
There are three kinds of regular polyhedral groups, the tetrahedral, octahedral and icosahedral groups. Take one of them and write it, say G. Let M be the corresponding regular polyhedra and let p,q,r be the number of vertices of M, that of edges and that of faces, respectively. Then there is a reflection group W of rank four with the condition: the degrees of basic invariants coincide with 2,p,q,r. The first purpose of this paper is to show a relationship among the invariants of W and those of G. The second one is to introduce a system of equations of reflection group W and to give its solutions by reducing it to the homogenization of polyhedral equations for G introduced by Klein.