1 citations · 1 across the 4 of their papers we have counts for
4 papers
Proof of the Voronoi conjecture for 3-irreducible parallelotopes
Andrei Ordine
This article proves the Voronoi conjecture on parallelotopes in the special case of 3-irreducible tilings. Parallelotopes are convex polytopes which tile the Euclidean space by the…
A criterion of reducibility for a parallelohedron
Andrei Ordine, Alexander Magazinov
A parallelohedron is called reducible, if it can be represented as a direct product of two parallelohedra of lower dimension. In his Ph.D. thesis (2005) the first author proved a c…
Perfect Delaunay Polytopes and Perfect Quadratic Functions on Lattices
Robert Erdahl, Andrei Ordine, Konstantin Rybnikov
A polytope whose vertices belong to a lattice of rank is Delaunay if there is a circumscribing -dimensional ellipsoid, , with interior free of lattice points so that…
Perfect Delaunay Polytopes and Perfect Inhomogeneous Forms
Robert Erdahl, Andrei Ordine, Konstantin Rybnikov
A lattice Delaunay polytope D is called perfect if it has the property that there is a unique circumscribing ellipsoid with interior free of lattice points, and with the surface co…