Open AccessSymmetry group of the equiangular cubed sphere
Author(s) -
Jean-Baptiste Bellet
Publication year - 2021
Publication title -
quarterly of applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.603
H-Index - 41
eISSN - 1552-4485
pISSN - 0033-569X
DOI - 10.1090/qam/1604
Subject(s) - geodesic , mathematics , invariant (physics) , grid , group (periodic table) , rotational symmetry , cube (algebra) , symmetry group , combinatorics , symmetry (geometry) , circular symmetry , geometry , pure mathematics , physics , mathematical physics , quantum mechanics
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.