## Abstract

4-dimensional H4 polytopes and their dual polytopes have been constructed as the orbits of the Coxeter- Weyl group W(H _{4}) , where the group elements and the vertices of the polytopes are represented by quaternions. Projection of an arbitrary W(H _{4}) orbit into three dimensions is made preserving the icosahedral subgroup W(H _{3}) and the tetrahedral subgroup W(A _{3}) . The latter follows a branching under the Coxeter group W(A _{4}) . The dual polytopes of the semi-regular and quasi-regular H _{4} polytopes have been constructed.

Original language | English |
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Pages (from-to) | 309-333 |

Number of pages | 25 |

Journal | Turkish Journal of Physics |

Volume | 36 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2012 |

## Keywords

- 4D polytopes
- Coxeter groups
- Dual polytopes
- Quaternions
- W(H4)

## ASJC Scopus subject areas

- Physics and Astronomy(all)

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