### 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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**Branching of the W(H 4) polytopes and their dual polytopes under the coxeter groups W(A 4) and W(H 3) represented by quaternions.** / Koca, Mehmet; Koca, Nazife Özdeş; Al-Ajmi, Mudhahir.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Branching of the W(H 4) polytopes and their dual polytopes under the coxeter groups W(A 4) and W(H 3) represented by quaternions

AU - Koca, Mehmet

AU - Koca, Nazife Özdeş

AU - Al-Ajmi, Mudhahir

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - 4D polytopes

KW - Coxeter groups

KW - Dual polytopes

KW - Quaternions

KW - W(H4)

UR - http://www.scopus.com/inward/record.url?scp=84865241570&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84865241570&partnerID=8YFLogxK

U2 - 10.3906/fiz-1109-11

DO - 10.3906/fiz-1109-11

M3 - Article

VL - 36

SP - 309

EP - 333

JO - Turkish Journal of Physics

JF - Turkish Journal of Physics

SN - 1300-0101

IS - 3

ER -