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

Mehmet Koca; Nazife Ozdes Koca; Mudhahir Al-Ajmi

doi:10.1142/S0219887812500351

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

Mehmet Koca^*, Nazife Ozdes Koca, Mudhahir Al-Ajmi

^*Corresponding author for this work

Physics

Research output: Contribution to journal › Article › peer-review

12 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 language	English
Article number	1250035
Journal	International Journal of Geometric Methods in Modern Physics
Volume	9
Issue number	4
DOIs	https://doi.org/10.1142/S0219887812500351
Publication status	Published - Jun 2012

Keywords

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

ASJC Scopus subject areas

Physics and Astronomy (miscellaneous)

Access to Document

10.1142/S0219887812500351

Cite this

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

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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T1 - 4D-polytopes and their dual polytopes of the coxeter group W(A 4) represented by quaternions

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AU - Koca, Nazife Ozdes

AU - Al-Ajmi, Mudhahir

PY - 2012/6

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N2 - 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.

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 - dual polytopes

KW - quaternions

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