Abstract
We investigate the question of nonbasic Simplexes of an L-subdivision of five-dimensional lattices. It is shown that, apart from the Simplexes of volume 2V (V is the volume of the basic simplex), no other nonbasic L-simplexes exist in these lattices. In primitive lattices the L-simplexes of doubled volume abut the basic L-simplexes by 4-dimensional faces.
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G. F. Voronoi, Collected Papers in Three Volumes [in Russian], Vol. 2, Kiev (1952).
B. N. Delaunay, “Geometry of positive quadratic forms,” Uspekhi Matem. Nauk,3, 16–62 (1937);4, 102–164 (1938).
S. S. Ryshkov, Fundamentals of Extremal Problems of the Geometry of Positive Quadratic Forms [in Russian], Dissertation, Moscow (1970).
E. P. Baranovskii, “Simplexes of L-subdivisions of Euclidean spaces,” Matem. Zametki,10, No. 6, 659–670 (1971).
E. P. Baranovskii, “One theorem on L-subdivisions of point lattices,” Matem. Zametki,13, No. 4, 605–616 (1973).
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Translated from Matematicheskie Zametki, Vol. 13, No. 5, pp. 771–782, May, 1973.
In conclusion, the author wishes to thank S. S. ryshkov for participating in discusion of the result of this paper.
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Baranovskii, E.P. Volumes of L-simplexes of five-dimensional lattices. Mathematical Notes of the Academy of Sciences of the USSR 13, 460–466 (1973). https://doi.org/10.1007/BF01147478
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DOI: https://doi.org/10.1007/BF01147478