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Full-Text Articles in Physical Sciences and Mathematics
Branching Of The W(H_4) Polytopes And Their Dual Polytopes Under The Coxeter Groups W(A_4) And W(H_3) Represented By Quaternions, Mehmet Koca, Nazi̇fe Koca, Mudhahir Al-Ajmi
Branching Of The W(H_4) Polytopes And Their Dual Polytopes Under The Coxeter Groups W(A_4) And W(H_3) Represented By Quaternions, Mehmet Koca, Nazi̇fe Koca, Mudhahir Al-Ajmi
Turkish Journal of Physics
4-dimensional H_4 polytopes and their dual polytopes have been constructed as the orbits of the Coxeter-Weyl group W(H_4), where the group elements and the vertices of the polytopes are represented by quaternions. Projection of an arbitrary W(H_4) orbit into three dimensions is made preserving the icosahedral subgroup W(H_3) and the tetrahedral subgroup W(A_3). The latter follows a branching under the Coxeter group W(A_4). The dual polytopes of the semi-regular and quasi-regular H_4 polytopes have been constructed.