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

Ermiş, Temel

doi:10.36753/MATHENOT.643969

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

Temel Ermiş (Eskişehir Osmangazi Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bilgisayar Bölümü, Eskişehir, Türkiye)

Mathematical Sciences and Applications E-Notes

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Yıl: 2020 Cilt: 8 Sayı: 2 Sayfa Aralığı: 96 - 109 Metin Dili: İngilizce DOI: 10.36753/MATHENOT.643969 İndeks Tarihi: 09-12-2021

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

Öz:

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 R3 endowed with these new metrics are the semi direct product of the translation group T(3) of R3 with the Euclidean symmetry groups of Rectified Archimedean Solids.

Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] Atiyah, M., Sutcliffe, P.: Polyhedra in Physics, Chemistry and Geometry. Milan Journal of Mathematics. 71, 33-58 (2003).
[2] Berger, M.: Geometry I. Springer-Verlag (2004).
[3] Berger, M.: Geometry II, Springer-Verlag (2009).
[4] Carrizales, J.M.M., Lopez, J.L.R., Pal, U., Yoshida M.M., Yacaman M.J.: The Completion of the Platonic Atomic Polyhedra: The Dodecahedron. Small. 3 (2), 351-355 (2006).
[5] Ermi¸s, T.: Düzgün Çokyüzlülerin Metrik Geometriler ˙Ile ˙Ili¸skileri Üzerine. Ph.D. Eski¸sehir Osmangazi University (2014).
[6] Ermi¸s, T., Kaya, R.: Isometries the of 3−Dimensional Maximum Space. Konuralp Journal of Mathematics. 3 (1), 103-114 (2015).
[7] Geli¸sgen, Ö., Kaya, R.: The Taxicab Space Group. Acta Mathematica Hungarica. 122 (1-2), 187-200 (2009).
[8] Geli¸sgen, Ö., Çolak, Z.: A Family of Metrics for Some Polyhedra. Automation Computers Applied Mathematics Scienti c Journal. 24 (1), 3-15 (2015).
[9] Geli¸sgen, Ö., Can Z.: On The Family of Metrics for Some Platonic and Archimedean Polyhedra. Konuralp Journal of Mathematics. 4 (2), 2533 (2016).
[10] Geli¸sgen, Ö., Yavuz, S.: Isometry Groups of Chamfered Cube and Chamfered Octahedron Spaces. Mathematical Sciences and Applications E-Notes. 7 (2), 174-182 (2019).
[11] Griffiths, D.: Introduction to Elementary Particles. Wiley - VCH (1987).
[12] Horvath, A. G.: Semi-indefinite inner product and generalized Minkowski spaces. Journal of Geometry and Physics. 60 (9), 1190-1208 (2010). [13] Horvath A. G.: Isometries of Minkowski geometries. Lin. Algebra and Its Appl. 512, 172-190 (2017).
[14] Lopez, J.L.R, Carrizales, J.M.M., Yacaman, M.J.: Low Dimensional Non-Crystallographic Metallic Nanostructures: Hrtem Simulation, Models and Experimental Results. Modern Physics Letters B. 20 (13), 725-751 (2006).
[15] Saller, H.: Operational Quantum Theory I-Nonrelativistic Structures.Springer-Verlag (2006).
[16] Schattschneider, D. J.: Taxicab group. Amer.Math. Monthly. 91, 423-428 (1984).
[17] Thompson, A.C.: Minkowski Geometry. Cambridge University Press, Cambridge (1996).
[18] http://dmccooey.com/polyhedra/RectifiedArchimedean.html

APA	Ermiş T (2020). Geometric Analysis of the Some Rectified Archimedean Solids Spaces via Their Isometry Groups. , 96 - 109. 10.36753/MATHENOT.643969
Chicago	Ermiş Temel Geometric Analysis of the Some Rectified Archimedean Solids Spaces via Their Isometry Groups. (2020): 96 - 109. 10.36753/MATHENOT.643969
MLA	Ermiş Temel Geometric Analysis of the Some Rectified Archimedean Solids Spaces via Their Isometry Groups. , 2020, ss.96 - 109. 10.36753/MATHENOT.643969
AMA	Ermiş T Geometric Analysis of the Some Rectified Archimedean Solids Spaces via Their Isometry Groups. . 2020; 96 - 109. 10.36753/MATHENOT.643969
Vancouver	Ermiş T Geometric Analysis of the Some Rectified Archimedean Solids Spaces via Their Isometry Groups. . 2020; 96 - 109. 10.36753/MATHENOT.643969
IEEE	Ermiş T "Geometric Analysis of the Some Rectified Archimedean Solids Spaces via Their Isometry Groups." , ss.96 - 109, 2020. 10.36753/MATHENOT.643969
ISNAD	Ermiş, Temel. "Geometric Analysis of the Some Rectified Archimedean Solids Spaces via Their Isometry Groups". (2020), 96-109. https://doi.org/10.36753/MATHENOT.643969

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. 10.36753/MATHENOT.643969
Chicago	Ermiş Temel Geometric Analysis of the Some Rectified Archimedean Solids Spaces via Their Isometry Groups. Mathematical Sciences and Applications E-Notes 8, no.2 (2020): 96 - 109. 10.36753/MATHENOT.643969
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, 2020, ss.96 - 109. 10.36753/MATHENOT.643969
AMA	Ermiş T Geometric Analysis of the Some Rectified Archimedean Solids Spaces via Their Isometry Groups. Mathematical Sciences and Applications E-Notes. 2020; 8(2): 96 - 109. 10.36753/MATHENOT.643969
Vancouver	Ermiş T Geometric Analysis of the Some Rectified Archimedean Solids Spaces via Their Isometry Groups. Mathematical Sciences and Applications E-Notes. 2020; 8(2): 96 - 109. 10.36753/MATHENOT.643969
IEEE	Ermiş T "Geometric Analysis of the Some Rectified Archimedean Solids Spaces via Their Isometry Groups." Mathematical Sciences and Applications E-Notes, 8, ss.96 - 109, 2020. 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 (2020), 96-109. https://doi.org/10.36753/MATHENOT.643969