Minkowski geometry is a non-Euclidean geometry in a finite number of dimensions. In a Minkowski geometry the unit ball is a symmetric, convex closed set instead of the usual sphere in Euclidean space. In [14], it is shown that there are some geometries which unit spheres are cuboctahedron and truncated octahedron-which are Archimedean solids-, they are also Minkowski geometries. In geometry determining the group of isometries of a space with a metric is a fundamental problem. In this article we show that the group of isometries of the 3−dimensional spaces covered by CO − metric and TO − 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.