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 | |
| Publication status | Published - Jun 2012 |
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Keywords
- 4D-polytopes
- Coxeter groups
- dual polytopes
- quaternions
- W(A )
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)
Cite this
4D-polytopes and their dual polytopes of the coxeter group W(A 4) represented by quaternions. / Koca, Mehmet; Koca, Nazife Ozdes; Al-Ajmi, Mudhahir.
In: International Journal of Geometric Methods in Modern Physics, Vol. 9, No. 4, 1250035, 06.2012.Research output: Contribution to journal › Article
}
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
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 -