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Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Symmetry group of the equiangular cubed sphere

Author: Jean-Baptiste Bellet
Journal: Quart. Appl. Math. 80 (2022), 69-86
MSC (2020): Primary 86A08, 86A10, 65M50, 20B30, 52B15
Published electronically: November 19, 2021
MathSciNet review: 4360550
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Abstract: 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.

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Additional Information

Jean-Baptiste Bellet
Affiliation: Université de Lorraine, CNRS, IECL, F-57000 Metz, France
MR Author ID: 925061

Keywords: Cubed sphere, spherical grid, symmetry, octahedral group
Received by editor(s): May 27, 2021
Received by editor(s) in revised form: October 4, 2021
Published electronically: November 19, 2021
Article copyright: © Copyright 2021 Brown University