Geodesic
Minimal cubature formulas of degree~$3$ for a torus in~${\mathbb R}^3$
Matematičeskie trudy, Tome 18 (2015) no. 2, pp. 49-60

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We construct minimal cubature formulas of degree 3 for a torus in ${\mathbb R}^3$. The cases of a degenerate torus with radius $r=1$ and a torus with arbitrary radius $r>1$ are considered separately. 
@article{MT_2015_18_2_a3,
     author = {M. V. Noskov and I. M. Fedotova},
     title = {Minimal cubature formulas of degree~$3$ for a torus in~${\mathbb R}^3$},
     journal = {Matemati\v{c}eskie trudy},
     pages = {49--60},
     publisher = {mathdoc},
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     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2015_18_2_a3/}
}
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M. V. Noskov; I. M. Fedotova. Minimal cubature formulas of degree~$3$ for a torus in~${\mathbb R}^3$. Matematičeskie trudy, Tome 18 (2015) no. 2, pp. 49-60. http://geodesic.mathdoc.fr/item/MT_2015_18_2_a3/