ISOMETRY GROUPS OF TRUNCATED TETRAKIS HEXAHEDRON AND TRUNCATED TRIAKIS OCTAHEDRON SPACES

Abstract

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 Min-kowski 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 octahe-dral group Oh and translation group T(3).

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