Zonotopes, dicings, and Voronoi's conjecture on parallelohedra
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Publication:1306931
DOI10.1006/eujc.1999.0294zbMath0938.52016OpenAlexW1974502808WikidataQ122927055 ScholiaQ122927055MaRDI QIDQ1306931
Publication date: 5 October 1999
Published in: European Journal of Combinatorics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/eujc.1999.0294
Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Lattice packing and covering (number-theoretic aspects) (11H31) Tilings in (n) dimensions (aspects of discrete geometry) (52C22)
Related Items (25)
Tailoring a pair of pants ⋮ Belt distance between facets of space-filling zonotopes ⋮ On \(\pi\)-surfaces of four-dimensional parallelohedra ⋮ Lifts for Voronoi cells of lattices ⋮ On the sum of a parallelotope and a zonotope ⋮ Isoperimetric problems for zonotopes ⋮ On the tropical Torelli map ⋮ Convex polyhedral tilings hidden in crystals and quasicrystals ⋮ On the Voronoi Conjecture for Combinatorially Voronoi Parallelohedra in Dimension 5 ⋮ Geometry of lifts of tilings of Euclidean spaces ⋮ Parallelohedra defined by quadratic forms ⋮ Sufficient enlargements of minimal volume for finite-dimensional normed linear spaces ⋮ A Polynomial Time Algorithm for Solving the Closest Vector Problem in Zonotopal Lattices ⋮ An upper bound for a valence of a face in a parallelohedral tiling ⋮ Layer superposition of the root lattice \(A_n\) ⋮ Voronoi conjecture for special free parallelotopes ⋮ On compact representations of Voronoi cells of lattices ⋮ Voronoĭ's conjecture and space tiling zonotopes ⋮ Properties of parallelotopes equivalent to Voronoi's conjecture ⋮ Parallelohedra: A retrospective and new results ⋮ On the density of sets avoiding parallelohedron distance 1 ⋮ Properties of faces of parallelohedra ⋮ The Voronoi conjecture for parallelohedra with simply connected \(\delta\)-surfaces ⋮ A class of affinely equivalent Voronoi parallelohedra ⋮ Fullerenes and disk-fullerenes
Cites Work
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- On linear systems with integral valued solutions
- On lattice dicing
- An extension of Voronoï's theorem on primitive parallelotopes
- The theory of quality translations with applications to tilings
- Generatrissa: the problems of Maxwell and Voronoi
- The classification of zonohedra by means of projective diagrams
- Convex bodies which tile space by translation
- Space‐filling zonotopes
- Space tiling zonotopes
- Combinatorial Properties of Associated Zonotopes
- On Zonotopes
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