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4D-POLYTOPES AND THEIR DUAL POLYTOPES OF THE COXETER GROUP W(A4) REPRESENTED BY QUATERNIONS
Preview AbstractFour-dimensional A4 polytopes and their dual polytopes have been constructed as the orbits of the Coxeter–Weyl group W(A4) where the group elements and the vertices of the polytopes are represented by quaternions. Projection of an arbitrary W(A4) orbit into three dimensions is made using the subgroup W(A3). A generalization of the Catalan solids for 3D-polyhedra has been developed and dual polytopes of the uniform A4 polytopes have been constructed.