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C-types of n-dimensional lattices and 5-dimensional primitive parallelohedra with application to the theory of coverings by Sergeĭ Sergeevich Ryshkov

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Published by American Mathematical Society in Providence, R.I .
Written in English


  • Geometry of numbers.,
  • Lattice theory.,
  • Forms, Quadratic.

Book details:

Edition Notes

Statementby S. S. Ryškov and E. P. Baranovskiĭ.
SeriesProceedings of the Steklov Institute of Mathematics ; 1978, issue 4, Trudy Matematicheskogo instituta imeni V.A. Steklova., 1978, issue 4.
ContributionsBaranovskiĭ, Evgeniĭ Petrovich, 1924- joint author.
LC ClassificationsQA1 .A413 no. 137, QA241.5 .A413 no. 137
The Physical Object
Paginationiv, 140 p. :
Number of Pages140
ID Numbers
Open LibraryOL4733160M
ISBN 100821830376
LC Control Number78021923

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C-types of N-dimensional Lattices and 5-dimensional Primitive Parallelohedra With Application to the Theory of Coverings (Proceedings of the Steklov Institute of Mathematics) by Sergei Sergeevich Ryshkov, E. P. Baranovskii. C-types of n-dimensional Lattices and 5-dimensional Primitive Parallelohedra (with application to the Theory of Covering), Trudy of Steklov’s Mathematical Institute, (Translated as: Proceedings of Steklov Institute of Mathematics , No 4.) (, Vol. )Cited by: 2. For n = 5 there are types of primitive parallelohedra (see [72], [49], and also [50] and [10]). The number of non-primitive parallelohedra amounts to thousands. A lattice is rigid if any of its sufficiently small deformations distinct from a homothety changes its L -type. Using the list of 84 zone-contracted Voronoi polytopes inR5given by Engel 8, we give a complete list of seven five-dimensional rigid lattices.

Enumerations of combinatorial types (i.e., L-types) of five-dimensional primitive lattices was performed in [6] five-dimensional primitive lattices wa Cited by: Sphere coverings, Lattices, and Tilings (In Low Dimensions) C-types of n-dimensional lattices and 5-dimensional primitive parallelohedra (with application to the theory of coverings)Author: Frank Vallentin. Abstract. The most important lattices in Euclidean space of dimension n≤ 8 are the lattices A n (n≥ 2), D n (n≥ 4), E n (n = 6, 7, 8) and their duals. In this paper we determine the cell structures of all these lattices and their Voronoi and Delaunay polytopes in a uniform by:   The concepts of a standard face of a parallelohedron and of the index of a face are introduced. It is shown that the sum of indices of standard faces in a parallelohedron is an invariant; this implies the Minkowski bound for the number of facets of parallelohedra. New properties of faces of parallelohedra are by:

lattices are explicitly introduced along with their combinatorial classi cation as an alternative to the symmetry classi cation of lattices introduced in the previous chapter. Such notions as corona, facet, and shortest vectors are de ned and their utility for description of arbitrary N-dimensional lattices is outlined. Modeling and identification of centered crystal lattices in three-dimensional space Kirsh D.V., Samara State Aerospace University Kupriyanov A.V. Image Processing Systems Institute, Russian Academy of Sciences Abstract. The paper offers a method that allows to model crystal lattices in . In three-dimensional space, there are 14 Bravais lattices. These are obtained by combining one of the seven lattice systems with one of the centering types. The centering types identify the locations of the lattice points in the unit cell as follows: Primitive (P): lattice points on the cell corners only (sometimes called simple). The Lattices of Six-Dimensional Euclidean Space By W. Plesken* and W. Hanrath Abstract. The lattices of full rank of the six-dimensional Euclidean space are classified according to their automorphism groups (Bravais classification). We find types of such lattices. I. Introduction. A lattice L in an Euclidean vector space E is given by the Z.