Branching of the W(H_4) polytopes and their dual polytopes under the coxeter groups W(A_4) and W(H_3) represented by quaternions

Authors

MEHMET KOCA
NAZİFE KOCA
MUDHAHIR AL-AJMI

DOI

10.3906/fiz-1109-11

Abstract

4-dimensional H_4 polytopes and their dual polytopes have been constructed as the orbits of the Coxeter-Weyl group W(H_4), where the group elements and the vertices of the polytopes are represented by quaternions. Projection of an arbitrary W(H_4) orbit into three dimensions is made preserving the icosahedral subgroup W(H_3) and the tetrahedral subgroup W(A_3). The latter follows a branching under the Coxeter group W(A_4). The dual polytopes of the semi-regular and quasi-regular H_4 polytopes have been constructed.

Keywords

4D polytopes, dual polytopes, coxeter groups, quaternions, W(H_4)

First Page

309

Last Page

333

Recommended Citation

KOCA, MEHMET; KOCA, NAZİFE; and AL-AJMI, MUDHAHIR (2012) "Branching of the W(H_4) polytopes and their dual polytopes under the coxeter groups W(A_4) and W(H_3) represented by quaternions," Turkish Journal of Physics: Vol. 36: No. 3, Article 1. https://doi.org/10.3906/fiz-1109-11
Available at: https://journals.tubitak.gov.tr/physics/vol36/iss3/1