Geodesic
Cubic manifolds in lattices
Izvestiya. Mathematics , Tome 44 (1995) no. 2, pp. 301-313.

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A study is made of cubic complexes, and in particular of cubic manifolds. Necessary and sufficient conditions are obtained for a cubic manifold to be mapped into a standard cubic lattice. 
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N. P. Dolbilin; M. A. Shtan'ko; M. I. Shtogrin. Cubic manifolds in lattices. Izvestiya. Mathematics , Tome 44 (1995) no. 2, pp. 301-313. http://geodesic.mathdoc.fr/item/IM2_1995_44_2_a4/

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