1 citations · 3 across the 4 of their papers we have counts for
4 papers
On the sum of the Voronoi polytope of a lattice with a zonotope
Mathieu Dutour Sikiric, Viatcheslav Grishukhin, Alexander Magazinov
A parallelotope is a polytope that admits a facet-to-facet tiling of space by translation copies of along a lattice. The Voronoi cell of a lattice is an exampl…
The decomposition of the hypermetric cone into L-domains
Mathieu Dutour Sikiric, Viatcheslav Grishukhin
The hypermetric cone $\HYP_{n+1}$ is the parameter space of basic Delaunay polytopes in n-dimensional lattice. The cone $\HYP_{n+1}$ is polyhedral; one way of seeing this is that m…
How to compute the rank of a Delaunay polytope
Mathieu Dutour Sikiric, Viatcheslav Grishukhin
Roughly speaking, the rank of a Delaunay polytope (first introduced in \cite{DGL92}) is its number of degrees of freedom. In \cite{DL}, a method for computing the rank of a Delauna…
Properties of parallelotopes equivalent to Voronoi's conjecture
Michel Deza, Viacheslav Grishukhin
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…