Quaternionic construction of the W(F4) polytopes with their dual polytopes and branching under the subgroups W(B4) and W(B 3) × W(A1)

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Abstract

Four-dimensional F4 polytopes and their dual polytopes have been constructed as the orbits of the Coxeter-Weyl group W(F4 ) where the group elements and the vertices of the polytopes are represented by quaternions. Branchings of an arbitrary W(F4 ) orbit under the Coxeter groups W(B4) and W(B3) × W(A1) have been presented. The role of group theoretical technique and the use of quaternions have been emphasized.

Original languageEnglish
Article number1350010
JournalInternational Journal of Geometric Methods in Modern Physics
Volume10
Issue number5
DOIs
Publication statusPublished - May 2013

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polytopes
subgroups
quaternions
orbits
apexes

Keywords

  • 4D polytopes
  • Coxeter groups
  • dual polytopes
  • quaternions
  • W(F)

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

Cite this

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title = "Quaternionic construction of the W(F4) polytopes with their dual polytopes and branching under the subgroups W(B4) and W(B 3) × W(A1)",
abstract = "Four-dimensional F4 polytopes and their dual polytopes have been constructed as the orbits of the Coxeter-Weyl group W(F4 ) where the group elements and the vertices of the polytopes are represented by quaternions. Branchings of an arbitrary W(F4 ) orbit under the Coxeter groups W(B4) and W(B3) × W(A1) have been presented. The role of group theoretical technique and the use of quaternions have been emphasized.",
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author = "Mehmet Koca and Mudhahir Al-Ajmi and Koca, {Nazife Ozdes}",
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T1 - Quaternionic construction of the W(F4) polytopes with their dual polytopes and branching under the subgroups W(B4) and W(B 3) × W(A1)

AU - Koca, Mehmet

AU - Al-Ajmi, Mudhahir

AU - Koca, Nazife Ozdes

PY - 2013/5

Y1 - 2013/5

N2 - Four-dimensional F4 polytopes and their dual polytopes have been constructed as the orbits of the Coxeter-Weyl group W(F4 ) where the group elements and the vertices of the polytopes are represented by quaternions. Branchings of an arbitrary W(F4 ) orbit under the Coxeter groups W(B4) and W(B3) × W(A1) have been presented. The role of group theoretical technique and the use of quaternions have been emphasized.

AB - Four-dimensional F4 polytopes and their dual polytopes have been constructed as the orbits of the Coxeter-Weyl group W(F4 ) where the group elements and the vertices of the polytopes are represented by quaternions. Branchings of an arbitrary W(F4 ) orbit under the Coxeter groups W(B4) and W(B3) × W(A1) have been presented. The role of group theoretical technique and the use of quaternions have been emphasized.

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KW - dual polytopes

KW - quaternions

KW - W(F)

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