Geodesic
Affine Types of $L$-Polyhedra for 5-lattices
Matematičeskie zametki, Tome 71 (2002) no. 3, pp. 412-430

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We construct an algorithm for deducing all affinely nonequivalent types of $L$-polyhedra on $n$-lattices, where $n\le 5$. The computational part of the algorithm designed for calculations on a personal computer is based on the relationship between the geometry of lattices and the theory of hypermetric spaces. For the first time, a complete list of affine types (139 types) of $L$-polyhedra on 5-lattices is obtained. 
@article{MZM_2002_71_3_a7,
     author = {P. G. Kononenko},
     title = {Affine {Types} of $L${-Polyhedra} for 5-lattices},
     journal = {Matemati\v{c}eskie zametki},
     pages = {412--430},
     publisher = {mathdoc},
     volume = {71},
     number = {3},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_71_3_a7/}
}
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P. G. Kononenko. Affine Types of $L$-Polyhedra for 5-lattices. Matematičeskie zametki, Tome 71 (2002) no. 3, pp. 412-430. http://geodesic.mathdoc.fr/item/MZM_2002_71_3_a7/