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4d-polytopes described by Coxeter diagrams and quaternions

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, , Citation Mehmet Koca 2011 J. Phys.: Conf. Ser. 284 012040 DOI 10.1088/1742-6596/284/1/012040

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

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1742-6596/284/1/012040

Abstract

4D-polytopes and their dual polytopes can be described as the orbits of the rank-4 Coxeter-Weyl groups. Their symmetries follow from the quaternionic descriptions of the rank-4 Coxeter-Dynkin diagrams. There exists a one to one correspondence between the finite subgroups of quaternions and the rank-4 Coxeter-Weyl groups.

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10.1088/1742-6596/284/1/012040