Geometric Analysis of the Some Rectified Archimedean Solids Spaces via Their Isometry Groups

Year 2020, Volume: 8 Issue: 2, 96 - 109, 15.10.2020

Temel Ermiş

https://doi.org/10.36753/mathenot.643969

Abstract

There are two main motivations in this article. First,we give the new metrics and the metric spaces whose unit spheres are Rectified Archimedean Solids. Then, using the general technique which is quite simple, we show that isometry group of $\mathbb{R}^{3}$ endowed with these new metrics are the semi direct product of the translation group $T(3)$ of $\mathbb{R}^{3}\ $ with the Euclidean symmetry groups of Rectified Archimedean Solids.

                                                                                                                                                                                                                                             .

Keywords

Polyhedrons, Metric geometry, Isometry group, Octahedral group, Icosahedral group, Rectified Archimedean solids

Supporting Institution

ESKISEHIR OSMANGAZI UNIVERSTY

Project Number

201719A235

Thanks

This work was supported by the Scientific Research Projects Commission of Eskisehir Osmangazi University under Project Number 201719A235.

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