Ryshkov, S. S.; Erdahl, R. M. Dual systems of integral vectors. (General questions, applications to the geometry of positive quadratic forms). (Russian) Zbl 0751.52007 Mat. Sb. 182, No. 12, 1796-1821 (1991). This paper is in connection with the theory of \(L\)-decompositions of the \(n\)-dimensional lattice-like point systems. The authors introduce some new concepts for the set of integral vectors, they define the “dual” and “closed” systems and the “arithmetic \(L\)-body”. Using the basic properties of these concepts they examine the following question, whether a given arithmetic \(L\)-body can be realized in the \(n\)-dimensional Euclidean space or not. For small \(n\) \((n\leq 5)\) the authors have solved this problem and described all affine types of \(L\)-polyhedra characterizing the \(n\)-dimensional lattices. Reviewer: Á.G.Horváth (Budapest) Cited in 3 ReviewsCited in 1 Document MSC: 52C07 Lattices and convex bodies in \(n\) dimensions (aspects of discrete geometry) 11H55 Quadratic forms (reduction theory, extreme forms, etc.) Keywords:\(L\)-decomposition; lattice; arithmetic \(L\)-body; \(L\)-polyhedra PDFBibTeX XMLCite \textit{S. S. Ryshkov} and \textit{R. M. Erdahl}, Mat. Sb. 182, No. 12, 1796--1821 (1991; Zbl 0751.52007) Full Text: EuDML