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4-dimensional H4 polytopes and their dual polytopes have been constructed asthe orbits of the Coxeter-Weyl group W(H4) where the group elements and thevertices of the polytopes are represented by quaternions. Projection of anarbitrary W(H4) orbit into three dimensions is made preserving the icosahedralsubgroup W(H3) and the tetrahedral subgroup W(A3), the latter follows abranching under the Coxeter group W(A4) . The dual polytopes of thesemi-regular and quasi-regular H4 polytopes have been constructed.

Branching of the W(H4) Polytopes and Their Dual Polytopes under the Coxeter Groups W(A4) and W(H3) Represented by Quaternions