The second Voronoi conjecture on parallelohedra for zonotopes

Details The second Voronoi conjecture on parallelohedra for zonotopes The second Voronoi conjecture on parallelohedra for zonotopes

2011-04-03

arxiv.org/abs/1104.0401v2

Moscow Journal of Combinatorics and Number Theory, 2011, vol. 1, issue 2, pp. 33-39

Mathematics

Combinatorics

6 pages, available in English or Russian

Scientific paper

We prove the second Voronoi conjecture on parallelohedra for zonotope. We
show that for a given face-to-face tiling of d-dimensional Euclidean space into
parallel copies of zonotope Z there are d vectors, connecting centers of
zonotopes with common facet, that are basis of the correspondent lattice of the
tiling.

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