Group theoretical analysis of 600-cell and 120-cell 4D polytopes with quaternions

Mehmet Koca; Mudhahir Al-Ajmi; Ramazan Koç

doi:10.1088/1751-8113/40/27/013

Group theoretical analysis of 600-cell and 120-cell 4D polytopes with quaternions

Mehmet Koca^*, Mudhahir Al-Ajmi, Ramazan Koç

^*Corresponding author for this work

Physics

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

600-cell {3, 3, 5} and 120-cell {5, 3, 3} four-dimensional dual polytopes relevant to quasicrystallography have been studied with the quaternionic representation of the Coxeter group W(H₄). The maximal subgroups W(SU(5)):Z₂ and W(H₃) × Z₂ of W(H ₄) play important roles in the analysis of cell structures of the dual polytopes. In particular, the Weyl-Coxeter group W(SU(4)) is used to determine the tetrahedral cells of the polytope {3, 3, 5}, and the Coxeter group W(H₃) is used for the dodecahedral cells of {5, 3, 3}. Using the Lie algebraic techniques in terms of quaternions, we explicitly construct cell structures forming the vertices of the 4D polytopes.

Original language	English
Article number	013
Pages (from-to)	7633-7642
Number of pages	10
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	40
Issue number	27
DOIs	https://doi.org/10.1088/1751-8113/40/27/013
Publication status	Published - Jul 6 2007

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Statistics and Probability
Modelling and Simulation
Mathematical Physics
General Physics and Astronomy

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abstract = "600-cell {3, 3, 5} and 120-cell {5, 3, 3} four-dimensional dual polytopes relevant to quasicrystallography have been studied with the quaternionic representation of the Coxeter group W(H4). The maximal subgroups W(SU(5)):Z2 and W(H3) × Z2 of W(H 4) play important roles in the analysis of cell structures of the dual polytopes. In particular, the Weyl-Coxeter group W(SU(4)) is used to determine the tetrahedral cells of the polytope {3, 3, 5}, and the Coxeter group W(H3) is used for the dodecahedral cells of {5, 3, 3}. Using the Lie algebraic techniques in terms of quaternions, we explicitly construct cell structures forming the vertices of the 4D polytopes.",

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AU - Koç, Ramazan

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Group theoretical analysis of 600-cell and 120-cell 4D polytopes with quaternions

Abstract

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