TY  - JOUR
T1  - Isometry Groups of Chamfered Cube and Chamfered Octahedron Spaces
AU  - Gelişgen, Özcan
AU  - Yavuz, Serhat
PY  - 2019
DA  - October
Y2  - 2019
DO  - 10.36753/mathenot.542272
JF  - Mathematical Sciences and Applications E-Notes
JO  - Math. Sci. Appl. E-Notes
PB  - Murat TOSUN
WT  - DergiPark
SN  - 2147-6268
SP  - 174
EP  - 182
VL  - 7
IS  - 2
LA  - en
AB  - Polyhedra have interesting symmetries. Therefore they have attracted the attention of scientists andartists from past to present. Thus polyhedra are discussed in a lot of scientific and artistic works. There areonly five regular convex polyhedra known as the platonic solids. There are many relationships betweenmetrics and polyhedra. Some of them are given in previous studies. In this study, we introduce two newmetrics, and show that the spheres of the 3-dimensional analytical space furnished by these metrics arechamfered cube and chamfered octahedron. Also we give some properties about these metrics. We showthat the group of isometries of the 3-dimesional space covered by CC􀀀metric and CO􀀀metric are thesemi-direct product of Oh and T(3), where octahedral group Oh is the (Euclidean) symmetry group of theoctahedron and T(3) is the group of all translations of the 3-dimensional space.
KW  - Polyhedron
KW  - Metric
KW  - Isometry Group
KW  - Octahedral Symmetry
KW  - Chamfered Cube
KW  - Chamfered Octahedron
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UR  - https://doi.org/10.36753/mathenot.542272
L1  - https://dergipark.org.tr/en/download/article-file/833552
ER  -