Repeated patterns of dense packings of equal disks in a square.
Représentation des fonctions affines semi-continues inférieurement
Représentation intégrale dans certains convexes
Représentation intégrale dans des sous-espaces de fonctions à valeurs vectorielles
Representation of curves of constant width in the hyperbolic plane.
Representation theorem for convex effect algebras
Effect algebras have important applications in the foundations of quantum mechanics and in fuzzy probability theory. An effect algebra that possesses a convex structure is called a convex effect algebra. Our main result shows that any convex effect algebra admits a representation as a generating initial interval of an ordered linear space. This result is analogous to a classical representation theorem for convex structures due to M.H. Stone.
Rep-tiling Euclidean space.
Residual Finiteness of Surface Groups via Tessellations.
Resultados recientes sobre mosaicos de Penrose.
Résumé de recherches sur la symétrie des polyèdres non eulériens.
Retour sur les caractères fermé et relativement ouvert du cône-barrière d'un convexe
Rhombus tilings of a hexagon with two triangles missing on the symmetry axis.
Riemann sums over polytopes
It is well-known that the -th Riemann sum of a compactly supported function on the real line converges to the Riemann integral at a much faster rate than the standard rate of convergence if the sum is over the lattice, . In this paper we prove an n-dimensional version of this result for Riemann sums over polytopes.
Rigidity and Energy.
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 and the lower bound Theorem l.
Rigidity of infinite disk patterns.
Rigidity of planar tilings.
Rigidity of planar tilings (Erratum).