- Mathematical Sciences and Applications E-Notes
- Vol: 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
Authors : Temel ERMİŞ
Pages : 96-109
Doi:10.36753/mathenot.643969
View : 6 | Download : 3
Publication Date : 2020-10-15
Article Type : Research
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