AbstractThis article applies group theory to the problem of calculating accurate cubature grids for three‐dimensional (3D) integrals that have an exponential weighting factor. The nodes of a cubature are divided into structures, each with the full symmetry of the octahedral group. The sequence of structures is derived from a basis set of polynomials forming a Sturmian basis for the function space. Several cubatures, of up to eighth degree accuracy, are reported and their features discussed. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005