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QUATERNIONIC CONSTRUCTION OF THE W(F₄) POLYTOPES WITH THEIR DUAL POLYTOPES AND BRANCHING UNDER THE SUBGROUPS W(B₄) AND W(B₃) × W(A₁)

Department of Physics, College of Science, Sultan Qaboos University, P. O. Box 36, Al-Khoud 123, Muscat, Sultanate of Oman

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MUDHAHIR AL-AJMI

Department of Physics, College of Science, Sultan Qaboos University, P. O. Box 36, Al-Khoud 123, Muscat, Sultanate of Oman

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, and

NAZIFE OZDES KOCA

Department of Physics, College of Science, Sultan Qaboos University, P. O. Box 36, Al-Khoud 123, Muscat, Sultanate of Oman

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https://doi.org/10.1142/S0219887813500102Cited by:1 (Source: Crossref)

Abstract

Four-dimensional F₄ polytopes and their dual polytopes have been constructed as the orbits of the Coxeter–Weyl group W(F₄ ) where the group elements and the vertices of the polytopes are represented by quaternions. Branchings of an arbitrary W(F₄ ) orbit under the Coxeter groups W(B₄) and W(B₃) × W(A₁) have been presented. The role of group theoretical technique and the use of quaternions have been emphasized.

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