4D-polytopes and their dual polytopes of the coxeter group W(A ₄) represented by quaternions

Four-dimensional A ₄ polytopes and their dual polytopes have been constructed as the orbits of the CoxeterWeyl group W(A ₄) where the group elements and the vertices of the polytopes are represented by quaternions. Projection of an arbitrary W(A ₄) orbit into three dimensions is made using the subgroup W(A ₃). A generalization of the Catalan solids for 3D-polyhedra has been developed and dual polytopes of the uniform A ₄ polytopes have been constructed.