4D-polytopes and their dual polytopes of the coxeter group W(A 4) represented by quaternions

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10 Citations (Scopus)

Abstract

Four-dimensional A 4 polytopes and their dual polytopes have been constructed as the orbits of the CoxeterWeyl group W(A 4) where the group elements and the vertices of the polytopes are represented by quaternions. Projection of an arbitrary W(A 4) orbit into three dimensions is made using the subgroup W(A 3). A generalization of the Catalan solids for 3D-polyhedra has been developed and dual polytopes of the uniform A 4 polytopes have been constructed.

Original languageEnglish
Article number1250035
JournalInternational Journal of Geometric Methods in Modern Physics
Volume9
Issue number4
DOIs
Publication statusPublished - Jun 2012

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polytopes
quaternions
orbits
subgroups
polyhedrons
apexes
projection

Keywords

  • 4D-polytopes
  • Coxeter groups
  • dual polytopes
  • quaternions
  • W(A )

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

Cite this

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abstract = "Four-dimensional A 4 polytopes and their dual polytopes have been constructed as the orbits of the CoxeterWeyl group W(A 4) where the group elements and the vertices of the polytopes are represented by quaternions. Projection of an arbitrary W(A 4) orbit into three dimensions is made using the subgroup W(A 3). A generalization of the Catalan solids for 3D-polyhedra has been developed and dual polytopes of the uniform A 4 polytopes have been constructed.",
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author = "Mehmet Koca and Koca, {Nazife Ozdes} and Mudhahir Al-Ajmi",
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AU - Koca, Mehmet

AU - Koca, Nazife Ozdes

AU - Al-Ajmi, Mudhahir

PY - 2012/6

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AB - Four-dimensional A 4 polytopes and their dual polytopes have been constructed as the orbits of the CoxeterWeyl group W(A 4) where the group elements and the vertices of the polytopes are represented by quaternions. Projection of an arbitrary W(A 4) orbit into three dimensions is made using the subgroup W(A 3). A generalization of the Catalan solids for 3D-polyhedra has been developed and dual polytopes of the uniform A 4 polytopes have been constructed.

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KW - quaternions

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