Radiography of perfect lattices. (Radiographie des réseaux parfaits.)
Rangements optimaux de carrés unité dans une bande infinie
Rank forms, closed zones and laminae
For a given lattice, we establish an equivalence between closed zones for the corresponding Voronoï polytope, suitable hyperplane sections of the corresponding Delaunay partition, and rank quadratic forms which are extreme rays for the corresponding -type domain.
Rareté des intervalles recouvrant un point dans un recouvrement aléatoire
Rational model of the subspace complement on atomic complexes.
Rational realization of the minimum ranks of nonnegative sign pattern matrices
A sign pattern matrix (or nonnegative sign pattern matrix) is a matrix whose entries are from the set (, respectively). The minimum rank (or rational minimum rank) of a sign pattern matrix is the minimum of the ranks of the matrices (rational matrices, respectively) whose entries have signs equal to the corresponding entries of . Using a correspondence between sign patterns with minimum rank and point-hyperplane configurations in and Steinitz’s theorem on the rational realizability of...
Relative Newton Numbers.
Remarks on self-affine tilings.
Remarks on sphere packings, clusters and Hales Ferguson theorem
Remarks on the closest packing of convex discs.
Repeated patterns of dense packings of equal disks in a square.
Rep-tiling Euclidean space.
Residual Finiteness of Surface Groups via Tessellations.
Resultados recientes sobre mosaicos de Penrose.
Rhombus tilings of a hexagon with two triangles missing on the symmetry axis.
Rigidity and flexibility of virtual polytopes
All 3-dimensional convex polytopes are known to be rigid. Still their Minkowski differences (virtual polytopes) can be flexible with any finite freedom degree. We derive some sufficient rigidity conditions for virtual polytopes and present some examples of flexible ones. For example, Bricard's first and second flexible octahedra can be supplied by the structure of a virtual polytope.
Rigidity and the Alexandrov-Fenchel Inequality.
Rigidity of infinite disk patterns.
Rigidity of planar tilings.
Rigidity of planar tilings (Erratum).