10 citations · 41 across the 14 of their papers we have counts for
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Perfect Delaunay Polytopes in Low Dimensions
Mathieu Dutour, Robert Erdahl, Konstantin Rybnikov
A lattice Delaunay polytope is known as perfect if the only ellipsoid, that can be circumscribed about it, is its Delaunay sphere. Perfect Delaunay polytopes are in one-to-one corr…
Adjacency method for extreme Delaunay polytopes
Mathieu Dutour
The {\em hypermetric cone} is defined as the cone of semimetrics satisfying the {\em hypermetric inequalities}. Every {\em Delaunay polytope} corresponds to a ray of this polyhedra…
Some six-dimensional rigid forms
Mathieu Dutour, Frank Vallentin
One can always decompose Dirichlet-Voronoi polytopes of lattices non-trivially into a Minkowski sum of Dirichlet-Voronoi polytopes of rigid lattices. In this report we show how one…
Infinite serie of extreme Delaunay polytopes
M. Dutour
A Delaunay polytope is said to be {\em extreme} if the only (up to isometries) affine bijective transformations of , for which is again a Delaunay polytope, ar…
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…