Projection of Polyhedra onto Coxeter Planes Described with Quaternions

Mudhahir Al-Ajmi, Mehmet Koca, Hashima Bait Bu Salasel

Abstract


3-dimensional convex uniform polyhedra have been projected onto their corresponding Coxeter planes defined by the simple roots of the Coxeter diagram ,


Keywords


Coxeter group; Group Theory; Quaternions; Projection.

Full Text:

PDF

References


Coxeter, H.S.M. Regular Polytopes ( 3rd Edition). New York: Dover Publications., 1973, 33-57.

Zuber, J.B. Quantum Symmetries in Theoretical Physics and Mathematics (Bariloche, 2000) Contmp. Math. 294, Amer. Math. Soc., Providence , RI.

Hamilton, W.R. 1853. Lectures on Quaternions. London: Whittaker.

Koca, M., Koc, R. and Al-Ajmi, M. Polyhedra obtained from Coxeter groups and quaternions. J. Math. Phys., 2007, 48, 113514-113527.

Koca, M., Koc, R. and Al-Barwani, M. Quaternionic root systems and subgroups of the Aut(F4). J. Math. Phys., 2006, 47, 043507.

Koca, M., Koca, N.O. and Al-Ajmi, M. Branching of the W(H4) polytopes and their dual polytopes under the Coxeter groups W(A4) and W(H3) represented by quaternions. Turk. J. Phys., 2012, 36, 309-333.

Koca, M., Koc, R. and Al-Ajmi, M. Group theoretical analysis of 4D polytopes 600-cell and 120-cell with quaternions. J. Phys. A: Math. and Theor., 2007, 40, 7633.

Koca, M., Koc, R. and Al-Ajmi, M. Quaternionic representation of the Coxeter group H4 and the polyhedra. J. Phys. A: Math. Gen., 2006, 39, 14047-14054.

Koca, M., Koca, N.O. and Al-Shu'eili, M. Chiral polyhedra derived from Coxeter diagrams and quaternions. SQU J. Sci., 2011, 16, 63-82.

Koca, M., Koca, N.O. and Koc, R. Catalan solids derived from 3D-root systems. J. Math. Phys., 2010, 51, 043501.




DOI: http://dx.doi.org/10.24200/squjs.vol19iss2pp77-90

Refbacks

  • There are currently no refbacks.


Copyright (c) 2017 Mudhahir Al-Ajmi, Mehmet Koca, Hashima Bait Bu Salasel

Creative Commons License
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.

SQUJS 2017-CC BY-ND

This journal and its content is licensed under a Attribution-NoDerivatives 4.0 International.

Flag Counter