ON THE ISOMETRIES OF 3-DIMENSIONAL MAXIMUM SPACE

Abstract

In this article, the hexahedron associated to metric geometry full- led by the metric of which unit sphere is hexahedron. We have analytically proved that the isometry group of the space with respect to this metric is the semi direct product of the Euclidean symmetry group of the cube and T(3) which is all translations of analytical 3􀀀space.

Keywords

• maximum distance,maximum space,isometry group

References

1. [1] Carrizales J. M. M. , Lopez J. L. R. , Pal U. , Yoshida M. M. and Yacaman M. J., The Completion of the Platonic Atomic Polyhedra: The Dodecahedron, Small Volume 2, Issue 3, pages 351 { 355, 2006.
2. [2] Fenn, R., Geometry, Springer Undergraduate Mathematics Series, 2003.
3. [3] Gelisgen,  O. , Kaya, R. , The Taxicab Space Group, Acta Mathematica Hungarica, Vol. 122, No.1-2, 187-200, 2009.
4. [4] Kaya, R. , Gelisgen,  O. , Ekmekci, S. , Bayar A. , Group of Isometries of CC-Plane, MJMS. , Vol. 18, No. 3 , 221-233, 2006.
5. [5] Kaya, R. , Gelisgen,  O. , Ekmekci, S. , Bayar A. , On The Group of Isometries of The Plane with Generalized Absolute Value Metric, Rocky Mountain Journal of Mathematics, Vol. 39, No. 2, 591-603, 2009.
6. [6] Lopez J. L. R, Carrizales J. M. M. and Yacaman M. J. , Low Dimensional Non - Crystallographic Metallic Nanostructures: Hrtem Simulation, Models and Experimental Results, Modern Physics Letters B. , Vol. 20, No. 13, 725-751, 2006.
7. [7] Martin, G. E. , Transformation Geometry, Springer-Verlag, 1997.
8. [8] Millman, R. S. , Parker, G.D., Geometry, A Metric Approach with Models, Undergraduate Texts in Mathematics, Springer-Verlag, 1981.

9. [9] Salihova, S., \Maksimum Metrik Geometri Uzerine", Eskisehir Osmangazi University, PhD Thesis, 2006.
10. [10] Schattschneider, D. J. , Taxicab group, Amer. Math. Monthly, 91, 423-428, 1984.