It is shown that the group of isometries of the 3-dimensional space with respect to taxicab metric is the semi-direct product of octahedral group O h and T (3), where O h is the (Euclidean) symmetry group of the regular octahedron and T (3) is the group of all translations of the 3-dimensional space.

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In this article, we, firstly, find that the spheres in the Chinese Checkers space are deltoidal icositetrahedrons. Then we show that the group of isometries of the 3-dimensional space with respect to Chinese Checkers metric is the semi-direct product of deltoidal icositetrahedron group G(D) and T (3), where G(D) is the (Euclidean) symmetry group of the deltoidal icositetrahedron and T (3) is the group of all translations of the 3-dimensional space.

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