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Baranovskiĭ, E. P.; Ryshkov, S. S.

On a second local minimum of the density of the lattice covering of a four-dimensional Euclidean space by similar spheres. (English. Russian original) Zbl 0158.29902

Sib. Math. J. 7, 583-590 (1966); translation from Sib. Mat. Zh. 7, 731-739 (1966).
Reviewer: H. Groemer
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scan of Zbl 0158.29902

MSC:

11H31 Lattice packing and covering (number-theoretic aspects)
52C17 Packing and covering in \(n\) dimensions (aspects of discrete geometry)

Keywords:

second local minimum; density of lattice covering; four-dimensional Euclidean space by similar spheres
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References:

[1] R. P. Bambah, On lattice covering by spheres, Proc. Nat. Inst. Sci., India,20, 25-52 (1954). · Zbl 0059.16301
[2] E. S. Barnes, The covering of space by spheres, Canadian J. Math.,8, No. 2, 293-304 (1956). · Zbl 0072.03603 · doi:10.4153/CJM-1956-033-4
[3] A. F. Gametskii, On the theory of covering Euclidean 4-space by identical spheres, Doklady Akad. Nauk SSSR,146, No. 5, 991-994 (1962).
[4] A. F. Gametskii, On the optimality of the principal lattice of the first type of Voronoi among lattices of the first type of arbitrary number of dimensions, Doklady Akad. Nauk SSSR,151, No. 3, 482-484 (1963).
[5] B. N. Delone and S. S. Ryshkov, Solution of the problem of the least dense lattice covering of 4-space by identical spheres, Doklady Akad. Nauk SSSR,152, No. 3, 523-524 (1963).
[6] B. N. Delone, Geometry of positive quadratic forms, Uspekhi Matem. Nauk,3, 16-62 (1937).
[7] G. F. Voronoi, Collected Works in Three Volumes [in Russian],2, Izd. Ak. Nauk UkrSSR, Kiev (1952).
[8] S. S. Ryshkov, Construction of an n-dimensional parallelepiped of the first type, Doklady Akad. Nauk SSSR,146, No. 5, 1027-1030 (1962).
[9] S. S. Ryshkov, Some remarks on the types of n-dimensional parallelepipeds and on the density of lattice coverings of the space En by identical spheres, Doklady Akad. Nauk SSSR,162, No. 2, 277-281 (1965).
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