10 citations · 33 across the 16 of their papers we have counts for
16 papers
Delaunay polytopes derived from the Leech lattice
Mathieu Dutour Sikiric, Konstantin Rybnikov
Given a lattice L of R^n, a polytope D is called a Delaunay polytope in L if the set of its vertices is S\cap L where S is a sphere having no lattice points in its interior. D is c…
Perfect but not generating Delaunay polytopes
Mathieu Dutour Sikiric, Konstantin Rybnikov
In his seminal 1951 paper "Extreme forms" Coxeter \cite{cox51} observed that for one can add vectors to the perfect lattice $\sfA_9$ so that the resulting perfect lattice…
A New Algorithm in Geometry of Numbers
Mathieu Dutour, Konstantin Rybnikov
A lattice Delaunay polytope P is called perfect if its Delaunay sphere is the only ellipsoid circumscribed about P. We present a new algorithm for finding perfect Delaunay polytope…
Convexity of Hypersurfaces in Spherical Spaces
Konstantin Rybnikov
A spherical set is called convex if for every pair of its points there is at least one minimal geodesic segment that joins these points and lies in the set. We prove that for n >=…
An Efficient Local Approach to Convexity Testing of Piecewise-Linear Hypersurfaces
Konstantin Rybnikov
We show that a closed piecewise-linear hypersurface immersed in () is the boundary of a convex body if and only if every point in the interior of each -face ha…
Perfect Delaunay Polytopes in Low Dimensions
Mathieu Dutour, Robert Erdahl, Konstantin Rybnikov
A lattice Delaunay polytope is known as perfect if the only ellipsoid, that can be circumscribed about it, is its Delaunay sphere. Perfect Delaunay polytopes are in one-to-one corr…