Projection of Polyhedra onto Coxeter Planes Described with Quaternions

3-dimensional convex uniform polyhedra have been projected onto their corresponding Coxeter planes defined by the simple roots of the Coxeter diagram I2(h). The projected vertices of a polyhedron onto its corresponding Coxeter plane constitute an orbit of the dihedral group . In this paper, we use the quaternionic representations of the Coxeter group elements and the vertices of the polyhedra.