Group of Isometries of the CC-Plane

Abstract

In this work, it is shown that the group of isometries of the plane with respect to the Chinese Checkers metric is the semi-direct product of the Dihedral group $D_8$ and $T(2)$, where $D_8$ is the (Euclidean) symmetry group of the regular octagon and $T(2)$ is the group of all translations of the plane. Furthermore, some properties of the CC-plane are studied and the area formula for a triangle is given.