Geodesic
Symmetric cubature formulas for a truncated octahedron
Matematičeskie zametki, Tome 14 (1973) no. 5, pp. 667-675.

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For a truncated octahedron, which can be used to fill the whole space $\mathbf{R}^3$ by translating it, we construct symmetric cubature formulas, exact for polynomials of degrees 3, 5, and 7. We furnish estimates of the remainder terms, and we discuss the problem of numerical integration over an arbitrary bounded domain $D\subset\mathbf{R}^3$. 
@article{MZM_1973_14_5_a6,
     author = {A. V. Yakovlev},
     title = {Symmetric cubature formulas for a truncated octahedron},
     journal = {Matemati\v{c}eskie zametki},
     pages = {667--675},
     publisher = {mathdoc},
     volume = {14},
     number = {5},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_14_5_a6/}
}
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A. V. Yakovlev. Symmetric cubature formulas for a truncated octahedron. Matematičeskie zametki, Tome 14 (1973) no. 5, pp. 667-675. http://geodesic.mathdoc.fr/item/MZM_1973_14_5_a6/