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

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2 Citations (Scopus)

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 languageEnglish
Pages (from-to)309-333
Number of pages25
JournalTurkish Journal of Physics
Volume36
Issue number3
DOIs
Publication statusPublished - 2012

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polytopes
quaternions
subgroups
orbits
preserving
apexes
projection

Keywords

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

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

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title = "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",
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.",
keywords = "4D polytopes, Coxeter groups, Dual polytopes, Quaternions, W(H4)",
author = "Mehmet Koca and Koca, {Nazife {\"O}zdeş} and Mudhahir Al-Ajmi",
year = "2012",
doi = "10.3906/fiz-1109-11",
language = "English",
volume = "36",
pages = "309--333",
journal = "Turkish Journal of Physics",
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publisher = "TUBITAK",
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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)

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DO - 10.3906/fiz-1109-11

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JF - Turkish Journal of Physics

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