Geodesic
Theorem on $L$-partitions of point lattices
Matematičeskie zametki, Tome 13 (1973) no. 4, pp. 605-616.

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It is shown that if a simplex $S$ is a basic $L$-simplex for a point lattice in $E^n$ ($n\le5$), then the lattice's $L$-simplexes that are contiguous to $S$ by $(n-1)$-faces can have as vertices lattice points belonging to a specified set of points $P(S)$, and a complete description of this set is given. Based on the fact that the set $P(S)$ is known, a new method of deriving the types of point lattices, different from the known methods (G. F. Voronoi's algorithm and B. N. Delaunay's method of layers), is obtained. The types of primitive lattices in $E^3$ and $E^4$ are derived by this method. 
@article{MZM_1973_13_4_a16,
     author = {E. P. Baranovskii},
     title = {Theorem on $L$-partitions of point lattices},
     journal = {Matemati\v{c}eskie zametki},
     pages = {605--616},
     publisher = {mathdoc},
     volume = {13},
     number = {4},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_13_4_a16/}
}
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E. P. Baranovskii. Theorem on $L$-partitions of point lattices. Matematičeskie zametki, Tome 13 (1973) no. 4, pp. 605-616. http://geodesic.mathdoc.fr/item/MZM_1973_13_4_a16/