Properties of parallelotopes equivalent to Voronoi’s conjecture

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Properties of parallelotopes equivalent to Voronoi's conjecture

A parallelotope is a polytope whose translation copies fill space without gaps and intersections by interior points. Voronoi conjectured that each parallelotope is an affine image of the Dirichlet domain of a lattice, which is a Voronoi polytope. We give several properties of a parallelotope and prove that each of them is equivalent to it is an affine image of a Voronoi polytope.

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ژورنال

عنوان ژورنال: European Journal of Combinatorics

سال: 2004

ISSN: 0195-6698

DOI: 10.1016/j.ejc.2003.09.012