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math.MG2003★ 1 cited
On locally convex PL-manifolds and fast verification of convexity
Konstantin Rybnikov
We show that a realization of a closed connected PL-manifold of dimension n-1 in Euclidean n-space (n>2) is the boundary of a convex polyhedron if and only if the interior of each…
math.MG2001
An Infinite Series of Perfect Quadratic Forms and Big Delaunay Simplexes in Z^n
Robert Erdahl, Konstantin Rybnikov
George Voronoi (1908-09) introduced two important reduction methods for positive quadratic forms: the reduction with perfect forms, and the reduction with L-type domains. A form is…