Year 2019, Volume 7 , Issue 2, Pages 174 - 182 2019-10-15

Isometry Groups of Chamfered Cube and Chamfered Octahedron Spaces

Özcan Gelişgen [1] , Serhat YAVUZ [2]


Polyhedra have interesting symmetries. Therefore they have attracted the attention of scientists and
artists from past to present. Thus polyhedra are discussed in a lot of scientific and artistic works. There are
only five regular convex polyhedra known as the platonic solids. There are many relationships between
metrics and polyhedra. Some of them are given in previous studies. In this study, we introduce two new
metrics, and show that the spheres of the 3-dimensional analytical space furnished by these metrics are
chamfered cube and chamfered octahedron. Also we give some properties about these metrics. We show
that the group of isometries of the 3-dimesional space covered by CC􀀀metric and CO􀀀metric are the
semi-direct product of Oh and T(3), where octahedral group Oh is the (Euclidean) symmetry group of the
octahedron and T(3) is the group of all translations of the 3-dimensional space.
Polyhedron, Metric, Isometry Group, Octahedral Symmetry, Chamfered Cube, Chamfered Octahedron
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Primary Language en
Journal Section Articles
Authors

Orcid: 0000-0001-7071-6758
Author: Özcan Gelişgen (Primary Author)
Institution: ESKİŞEHİR OSMANGAZİ ÜNİVERSİTESİ
Country: Turkey


Orcid: 0000-0003-4544-4257
Author: Serhat YAVUZ
Institution: ESKİŞEHİR OSMANGAZİ ÜNİVERSİTESİ
Country: Turkey


Dates

Publication Date : October 15, 2019

Bibtex @research article { mathenot542272, journal = {Mathematical Sciences and Applications E-Notes}, issn = {}, eissn = {2147-6268}, address = {}, publisher = {Murat TOSUN}, year = {2019}, volume = {7}, pages = {174 - 182}, doi = {10.36753/mathenot.542272}, title = {Isometry Groups of Chamfered Cube and Chamfered Octahedron Spaces}, key = {cite}, author = {Gelişgen, Özcan and YAVUZ, Serhat} }
APA Gelişgen, Ö , YAVUZ, S . (2019). Isometry Groups of Chamfered Cube and Chamfered Octahedron Spaces. Mathematical Sciences and Applications E-Notes , 7 (2) , 174-182 . DOI: 10.36753/mathenot.542272
MLA Gelişgen, Ö , YAVUZ, S . "Isometry Groups of Chamfered Cube and Chamfered Octahedron Spaces". Mathematical Sciences and Applications E-Notes 7 (2019 ): 174-182 <https://dergipark.org.tr/en/pub/mathenot/issue/49271/542272>
Chicago Gelişgen, Ö , YAVUZ, S . "Isometry Groups of Chamfered Cube and Chamfered Octahedron Spaces". Mathematical Sciences and Applications E-Notes 7 (2019 ): 174-182
RIS TY - JOUR T1 - Isometry Groups of Chamfered Cube and Chamfered Octahedron Spaces AU - Özcan Gelişgen , Serhat YAVUZ Y1 - 2019 PY - 2019 N1 - doi: 10.36753/mathenot.542272 DO - 10.36753/mathenot.542272 T2 - Mathematical Sciences and Applications E-Notes JF - Journal JO - JOR SP - 174 EP - 182 VL - 7 IS - 2 SN - -2147-6268 M3 - doi: 10.36753/mathenot.542272 UR - https://doi.org/10.36753/mathenot.542272 Y2 - 2019 ER -
EndNote %0 Mathematical Sciences and Applications E-Notes Isometry Groups of Chamfered Cube and Chamfered Octahedron Spaces %A Özcan Gelişgen , Serhat YAVUZ %T Isometry Groups of Chamfered Cube and Chamfered Octahedron Spaces %D 2019 %J Mathematical Sciences and Applications E-Notes %P -2147-6268 %V 7 %N 2 %R doi: 10.36753/mathenot.542272 %U 10.36753/mathenot.542272
ISNAD Gelişgen, Özcan , YAVUZ, Serhat . "Isometry Groups of Chamfered Cube and Chamfered Octahedron Spaces". Mathematical Sciences and Applications E-Notes 7 / 2 (October 2019): 174-182 . https://doi.org/10.36753/mathenot.542272
AMA Gelişgen Ö , YAVUZ S . Isometry Groups of Chamfered Cube and Chamfered Octahedron Spaces. Math. Sci. Appl. E-Notes. 2019; 7(2): 174-182.
Vancouver Gelişgen Ö , YAVUZ S . Isometry Groups of Chamfered Cube and Chamfered Octahedron Spaces. Mathematical Sciences and Applications E-Notes. 2019; 7(2): 182-174.