2 citations · 3 across the 4 of their papers we have counts for
5 papers
Minkowski sum of a Voronoi parallelotope and a segment
Robert Erdahl, Viacheslav Grishukhin
By a {\em Voronoi parallelotope} we mean a parallelotope determined by a non-negative quadratic form . It was studied by Voronoi in his famous memoir. For a set of vector…
Closure of principal L-type domain and its parallelotopes
Mathieu Dutour Sikiric, Viacheslav Grishukhin
Voronoi defined two polyhedral partitions of the cone of se\mi\de\fi\nite forms into L-type domains and into perfect domains. Up to equivalence, there is only one domain that is si…
Once more about the 52 four-dimensional parallelotopes
Michel Deza, Viacheslav Grishukhin
There are several works \cite{De} (and \cite{St}), \cite{En}, \cite{Co} and \cite{Va} enumerating four-dimensional parallelotopes. In this work we give a new enumeration showing th…
Once more about Voronoi's conjecture and space tiling zonotopes
Michel Deza, Viacheslav Grishukhin
Voronoi conjectured that any parallelotope is affinely equivalent to a Voronoi polytope. A parallelotope is defined by a set of facet vectors and defines a set of lat…
Non-rigidity degrees of root lattices and their duals
Michel Deza, Viacheslav Grishukhin
Non-rigidity degree of a lattice , nrd, is dimension of the L-type domain to which belongs. We complete here the table of nrd's of all root lattices and their duals; name…