• A
• A
• A
• ABC
• ABC
• ABC
• А
• А
• А
• А
• А
Regular version of the site

## The Voronoi conjecture for parallelohedra with simply connected δ-surfaces

Discrete and Computational Geometry. 2015. Vol. 53. No. 2. P. 245-260.
Garber A., Gavrilyuk A., Magazinov A.

We show that the Voronoi conjecture is true for parallelohedra with simply connected δ-surfaces. That is, we show that if the boundary of parallelohedron P remains simply connected after removing closed nonprimitive faces of codimension 2, then P is affinely equivalent to a Dirichlet–Voronoi domain of some lattice. Also, we construct the π-surface associated with a parallelohedron and give another condition in terms of a homology group of the constructed surface. Every parallelohedron with a simply connected δ-surface also satisfies the condition on the homology group of the π-surface.