### 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(H_{4}). The maximal subgroups W(SU(5)):Z_{2} and W(H_{3}) × Z_{2} 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(H_{3}) 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 | |

Publication status | Published - Jul 6 2007 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Modelling and Simulation
- Statistics and Probability

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*40*(27), 7633-7642. [013]. https://doi.org/10.1088/1751-8113/40/27/013

**Group theoretical analysis of 600-cell and 120-cell 4D polytopes with quaternions.** / Koca, Mehmet; Al-Ajmi, Mudhahir; Koç, Ramazan.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 40, no. 27, 013, pp. 7633-7642. https://doi.org/10.1088/1751-8113/40/27/013

}

TY - JOUR

T1 - Group theoretical analysis of 600-cell and 120-cell 4D polytopes with quaternions

AU - Koca, Mehmet

AU - Al-Ajmi, Mudhahir

AU - Koç, Ramazan

PY - 2007/7/6

Y1 - 2007/7/6

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=34250779822&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34250779822&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/40/27/013

DO - 10.1088/1751-8113/40/27/013

M3 - Article

VL - 40

SP - 7633

EP - 7642

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 27

M1 - 013

ER -