Properties of parallelotopes equivalent to Voronoi's conjecture

Details Properties of parallelotopes equivalent to Voronoi's conjecture Properties of parallelotopes equivalent to Voronoi's conjecture

2003-07-11

arxiv.org/abs/math/0307170v1

Mathematics

Metric Geometry

18 pages (submitted)

Scientific paper

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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