Symmetry group of the equiangular cubed sphere. (English) Zbl 1478.65093
Summary: 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 of the orthogonal transformations that leave the cubed sphere invariant. The main result is that it coincides with the symmetry group of a cube. The proposed proof emphasizes metric properties of the cubed sphere. We study the geodesic distance on the grid, which reveals that the shortest geodesic arcs match with the vertices of a cuboctahedron. The results of this paper lay the foundation for future numerical schemes, based on rotational invariance of the cubed sphere.
MSC:
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
| 86A10 | Meteorology and atmospheric physics |
| 65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
| 86-08 | Computational methods for problems pertaining to geophysics |
| 20B30 | Symmetric groups |
| 52B15 | Symmetry properties of polytopes |
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