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4D-POLYTOPES AND THEIR DUAL POLYTOPES OF THE COXETER GROUP W(A₄) REPRESENTED BY QUATERNIONS

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

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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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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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https://doi.org/10.1142/S0219887812500351Cited by:7 (Source: Crossref)

Abstract

Four-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.

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