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

Temel Ermiş

doi:10.36753/mathenot.643969

EN

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

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.

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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.

References

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[18] http://dmccooey.com/polyhedra/RectifiedArchimedean.html

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Temel Ermiş ^*
0000-0003-4430-5271
Türkiye

Publication Date

October 15, 2020

Submission Date

November 7, 2019

Acceptance Date

October 7, 2020

Published in Issue

Year 2020 Volume: 8 Number: 2

DOI

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

IZ

https://izlik.org/JA42XY54UD

APA

Ermiş, T. (2020). Geometric Analysis of the Some Rectified Archimedean Solids Spaces via Their Isometry Groups. Mathematical Sciences and Applications E-Notes, 8(2), 96-109. https://doi.org/10.36753/mathenot.643969

AMA

1.Ermiş T. Geometric Analysis of the Some Rectified Archimedean Solids Spaces via Their Isometry Groups. Math. Sci. Appl. E-Notes. 2020;8(2):96-109. doi:10.36753/mathenot.643969

Chicago

Ermiş, Temel. 2020. “Geometric Analysis of the Some Rectified Archimedean Solids Spaces via Their Isometry Groups”. Mathematical Sciences and Applications E-Notes 8 (2): 96-109. https://doi.org/10.36753/mathenot.643969.

EndNote

Ermiş T (October 1, 2020) Geometric Analysis of the Some Rectified Archimedean Solids Spaces via Their Isometry Groups. Mathematical Sciences and Applications E-Notes 8 2 96–109.

IEEE

[1]T. Ermiş, “Geometric Analysis of the Some Rectified Archimedean Solids Spaces via Their Isometry Groups”, Math. Sci. Appl. E-Notes, vol. 8, no. 2, pp. 96–109, Oct. 2020, doi: 10.36753/mathenot.643969.

ISNAD

Ermiş, Temel. “Geometric Analysis of the Some Rectified Archimedean Solids Spaces via Their Isometry Groups”. Mathematical Sciences and Applications E-Notes 8/2 (October 1, 2020): 96-109. https://doi.org/10.36753/mathenot.643969.

JAMA

1.Ermiş T. Geometric Analysis of the Some Rectified Archimedean Solids Spaces via Their Isometry Groups. Math. Sci. Appl. E-Notes. 2020;8:96–109.

MLA

Ermiş, Temel. “Geometric Analysis of the Some Rectified Archimedean Solids Spaces via Their Isometry Groups”. Mathematical Sciences and Applications E-Notes, vol. 8, no. 2, Oct. 2020, pp. 96-109, doi:10.36753/mathenot.643969.

Vancouver

1.Temel Ermiş. Geometric Analysis of the Some Rectified Archimedean Solids Spaces via Their Isometry Groups. Math. Sci. Appl. E-Notes. 2020 Oct. 1;8(2):96-109. doi:10.36753/mathenot.643969