10 citations · 21 across the 6 of their papers we have counts for
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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…
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…
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…
Data mining for cones of metrics, quasi-metrics, hemi-metrics and super-metrics
M. Deza, M. Dutour
Using some adaptations of the adjacency decomposition method \cite{CR} and the program {\it cdd} (~\cite{Fu}), we compute the first computationally difficult cases of convex cones…
The hypermetric cone on seven vertices
Mathieu Dutour, Michel Deza
The hypermetric cone is the set of vectors satisfying the inequalities $\sum_{1\leq i<j\leq n} b_ib_jd_{ij}\leq 0 with b_i\in\Z and \sum_{i=1}…
Embedding of regular tilings and star-honeycomb
M. Deza, M. I. Shtogrin
We review the regular tilings of d-sphere, Euclidean d-space, hyperbolic d-space and Coxeter's regular hyperbolic honeycombs (with infinite or star-shaped cells or vertex figures)…