We consider cubature formulas to approximate multivariate integrals that remain unchanged under the orientation preserving transformations of a cube. The use of invariant theory (Molien series, Reynold operator) for the construction of such cubature formulas is investigated. Some new cubature formulas for the unit cube that are obtained using this approach, are presented. © 2001 Elsevier Science B.V. All rights reserved.
Cools, R., & Kim, K. J. (2001). Rotation invariant cubature formulas over the n-dimensional unit cube. Journal of Computational and Applied Mathematics, 132(1), 15–32. https://doi.org/10.1016/S0377-0427(00)00595-1