419 research outputs found
New results on torus cube packings and tilings
We consider sequential random packing of integral translate of cubes
into the torus . Two special cases are of special
interest:
(i) The case which corresponds to a discrete case of tilings
(considered in \cite{cubetiling,book})
(ii) The case corresponds to a case of continuous tilings
(considered in \cite{combincubepack,book})
Both cases correspond to some special combinatorial structure and we describe
here new developments.Comment: 5 pages, conference pape
The complete classification of five-dimensional Dirichlet-Voronoi polyhedra of translational lattices
In this paper we report on the full classification of Dirichlet-Voronoi
polyhedra and Delaunay subdivisions of five-dimensional translational lattices.
We obtain a complete list of affine types (L-types) of Delaunay
subdivisions and it turns out that they are all combinatorially inequivalent,
giving the same number of combinatorial types of Dirichlet-Voronoi polyhedra.
Using a refinement of corresponding secondary cones, we obtain
contraction types. We report on details of our computer assisted enumeration,
which we verified by three independent implementations and a topological mass
formula check.Comment: 16 page
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