Branching of the W(H4) polytopes and their dual polytopes under the coxeter groups W(A4) and W(H3) represented by quaternions

Authors : Mehmet KOCA, Nazife Özdeş Koca And Mudhahir AL-AJMI

Pages : 309-333

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :4-dimensional H4 polytopes and their dual polytopes have been constructed as the orbits of the Coxeter-Weyl group Winsert ignore into journalissuearticles values(H4);, where the group elements and the vertices of the polytopes are represented by quaternions. Projection of an arbitrary Winsert ignore into journalissuearticles values(H4); orbit into three dimensions is made preserving the icosahedral subgroup Winsert ignore into journalissuearticles values(H3); and the tetrahedral subgroup Winsert ignore into journalissuearticles values(A3);. The latter follows a branching under the Coxeter group Winsert ignore into journalissuearticles values(A4);. The dual polytopes of the semi-regular and quasi-regular H4 polytopes have been constructed.
Keywords : 4D polytopes, dual polytopes, coxeter groups, quaternions, W H4,