Delaunay triangulation and triangulation of tori
Triangulations of the \(n\)-torus can be constructed from triangulations of the euclidean \(n\)-space which are invariant under a lattice. There is a standard triangulation which can be constructed from the cubical tessellation by triangulating each cube in the standard way. This was employed in the paper by the reviewer and \textit{G. Lassmann} in [Discrete Comput. Geom. 3, 169--176 (1988; Zbl 0634.52008)] for obtaining a triangulation of the \(n\)-torus with \(2^{n+1}- 1\) vertices. This is the minimum number so far obtained. For the 4-torus and the 8-torus the author constructed different triangulations with the same number of vertices. In the present paper the author starts from the Delaunay triangulation of a generic lattice in \(n\)-space. For the standard triangulation one can take the lattice \(A^*_n\). Each vertex link has \(2^{n+1}- 2\) vertices, thus suggesting the same minimum number of vertices as above.
scientific article; zbMATH DE number 5664574