### 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 |
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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