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

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Mathematical Sciences and Applications E-Notes
Volume:8 Issue:2
Geometric Analysis of the Some Rectified Archimedean Solids Spaces via Their Isometry Groups

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

Pages : 96-109

View : 38 | Download : 9

Publication Date : 2020-10-15

Article Type : Research Paper

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 $Tinsert ignore into journalissuearticles values(3);$ 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

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