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

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 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
dual polytopes
quaternions
W(A )

ASJC Scopus subject areas

Physics and Astronomy (miscellaneous)

Access to Document

10.1142/S0219887812500351

Fingerprint Dive into the research topics of '4D-polytopes and their dual polytopes of the coxeter group W(A 4) represented by quaternions'. Together they form a unique fingerprint.

Cite this

@article{caf0f758ab224f719968d6808780227e,

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.",

keywords = "4D-polytopes, Coxeter groups, dual polytopes, quaternions, W(A )",

author = "Mehmet Koca and Koca, {Nazife Ozdes} and Mudhahir Al-Ajmi",

year = "2012",

month = jun,

doi = "10.1142/S0219887812500351",

language = "English",

volume = "9",

journal = "International Journal of Geometric Methods in Modern Physics",

issn = "0219-8878",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "4",

}

TY - JOUR

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

AU - Koca, Mehmet

AU - Koca, Nazife Ozdes

AU - Al-Ajmi, Mudhahir

PY - 2012/6

Y1 - 2012/6

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.

KW - 4D-polytopes

KW - Coxeter groups

KW - dual polytopes

KW - quaternions

KW - W(A )

UR - http://www.scopus.com/inward/record.url?scp=84860440170&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860440170&partnerID=8YFLogxK

U2 - 10.1142/S0219887812500351

DO - 10.1142/S0219887812500351

M3 - Article

AN - SCOPUS:84860440170

VL - 9

JO - International Journal of Geometric Methods in Modern Physics

JF - International Journal of Geometric Methods in Modern Physics

SN - 0219-8878

IS - 4

M1 - 1250035

ER -