Geodesic
Invariant cubature formulas for the hyperoctahedron
Matematičeskie zametki, Tome 61 (1997) no. 5, pp. 734-741.

Voir la notice de l'article provenant de la source Math-Net.Ru

Cubature formulas for calculating integrals over the hyperoctahedron that are invariant under the group of all of its orthogonal transformations are obtained. Two of them are exact for all polynomials of degree no greater than seven and one is exact for all polynomials of degree no greater than five. 
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S. B. Stoyanova. Invariant cubature formulas for the hyperoctahedron. Matematičeskie zametki, Tome 61 (1997) no. 5, pp. 734-741. http://geodesic.mathdoc.fr/item/MZM_1997_61_5_a10/

[1] Mysovskikh I. P., Interpolyatsionnye kubaturnye formuly, Nauka, M., 1981 | Zbl

[2] Stroud A. H., Approximate calculation of multiple integrals, Prentice-Hall, Englewood Cliffs, New Jersey, 1971 | Zbl

[3] Sobolev S. L., “O formulakh mekhanicheskikh kubatur na poverkhnosti sfery”, Sib. matem. zh., 3:4 (1962), 769–796 | MR | Zbl