Symmetry group of the equiangular cubed sphere

The equiangular cubed sphere is a spherical grid, widely used in computational physics. This paper deals with mathematical properties of this grid. We identify the symmetry group,i.e.the group orthogonal transformations that leave invariant. main result it coincides cube. proposed proof emphasizes metric sphere. study geodesic distance on which reveals shortest arcs match vertices cuboctahedron. results lay foundation for future numerical schemes, based rotational invariance