On lattice dicing
A lattice dicing is a finite set \(\{G_ 1, \dots, G_ r\}\) of \(D\)- families of parallel hyperplanes in \(\mathbb{R}^ n\) which is both non- degenerate and vertex-regular, where the three needed terms are correspondingly defined as follows: A \(d\)-family contains an infinite number of equispaced parallel hyperplanes ``extending in both directions'', and the system \(\{G_ 1, \dots, G_ r\}\) is non- degenerate if it contains \(n\) \(D\)-families with linearly independent normal vectors; for the vertex-regularity we demand that each vertex of the dicing is contained in one hyperplane from each of the \(D\)-families. The authors investigate the relations of lattice dicings to the geometry of numbers, and they give a complete description of the possible lattice dicings in \(\mathbb{R}^ n\) with \(n \leq 5\).
scientific article; zbMATH DE number 683268