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- Title
ISOMETRY GROUPS OF TRUNCATED TETRAKIS HEXAHEDRON AND TRUNCATED TRIAKIS OCTAHEDRON SPACES.
- Authors
CAN, ZEYNEP; GELIŞGEN, ÖZCAN
- Abstract
One of the class of non-Euclidean geometries for a finite dimensions is Minkowski geometry. As well as known, only difference between Euclidean geometry and Minkowski geometry is the used distance function. For this reason, its unit ball of Minkowski geometry is a closed, certain symmetric, convex set which is different from sphere in Euclidean geometry. The truncated tetrakis hexahedron and the truncated triakis octahedron are convex solids in the class Truncated Catalan solids. The aim of this work is to develop two new Minkowski geometries by dTTH-metric and dTTO-metric which unit spheres are truncated tetrakis hexahedron and truncated triakis octahedron, respectively and to find their isometry groups. After we derive these metrics we also give some properties of them. Furthermore, we give that the group of isometries of the 3-dimensional analytical space furnished by dTTH-metric or dTTO-metric is the semi-direct product of octahedral group Oh and translation group T(3).
- Subjects
MINKOWSKI geometry; EUCLIDEAN geometry; NON-Euclidean geometry; UNIT ball (Mathematics); OCTAHEDRA; CATALAN numbers
- Publication
Scientific Studies & Research. Series Mathematics & Informatics, 2021, Vol 31, Issue 2, p131
- ISSN
2067-3566
- Publication type
Article