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. 
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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/

[1] Delone B. N., “Geometriya polozhitelnykh kvadratichnykh form”, UMN, 1937, no. 3, 16–62 ; 1938, no. 4, 102–164

[2] Erdahl R. M., Ryshkov S. S., “The empty sphere”, Can. J. Math., 39:4 (1987), 794–824 | MR | Zbl

[3] Baranovskii E. P., Vlasov E. V., Novikova N. V., Stroenie $L$-razbienii chetyrekhmernykh reshetok, Dep. VINITI No 78-V91, 1991, s. 1–38

[4] Baranovskii E. P., Kononenko P. G., “Ob odnom sposobe vyvoda $L$-mnogogrannikov $n$-mernykh reshetok”, Matem. zametki, 68:6 (2000), 830–841 | MR | Zbl

[5] Baranovskii E. P., Kononenko P. G., Dvukhsloinye $L$-mnogogranniki $5$-mernykh reshetok, Dep. VINITI No 387-V98, 1998, s. 1–28

[6] Assouad P., “Sur les inegalités valides dans $L^1$”, European J. Combin., 5 (1984), 99–112 | MR | Zbl

[7] Deza M., Grishukhin V. P., Laurent M., “Extreme hypermetric and $L$-polytopes” (Budapest, 1991), Colloq. Math. Soc. Janos Bolyai, 60, 157–209

[8] Deza M. (Tylkin M. E.), “O geometrii Khemminga edinichnykh kubov”, Dokl. AN SSSR, 134:5 (1960), 1037–1040 | MR

[9] Deza M., Grishukhin V. P., Laurent M., “The hypermetric cone is polyhedral”, Combinatorica, 13 (4) (1993), 397–411 | DOI | MR | Zbl

[10] Deza M., Grishukhin V. P., Laurent M., “Hypermetrics in Geometry of Numbers”, DIMACS Ser. in Disc. Math. and Theor. Comp. Sci., 20, 1995, 1–109 | MR | Zbl

[11] Avis D., Mutt, “All facets of the six-point Hamming cone”, European J. Combin., 10:4 (1989), 309–312 | MR | Zbl

[12] Baranovskii E. P., “Simpleksy $L$-razbienii evklidovykh prostranstv”, Matem. zametki, 10:6 (1971), 659–670 | MR | Zbl

[13] Baranovskii E. P., “Ob $L$-simpleksakh shestimernykh reshetok”, Vtoraya mezhdunarodnaya konferentsiya “Algebraicheskie, veroyatnostnye, geometricheskie, kombinatornye i funktsionalnye metody v teorii chisel” (25–30 sentyabrya 1995 g., Voronezh), 13 | Zbl

[14] Ryshkov S. S., Erdal R. M., “Poetazhnoe postroenie $L$-tel reshetok”, UMN, 44:2 (1989), 241–242 | MR