Parallelohedra: A retrospective and new results

DOI10.1090/S0077-1554-2013-00208-3zbMath1271.52013OpenAlexW2053088546MaRDI QIDQ2837773

Nikolai P. Dolbilin

Publication date: 11 July 2013

Published in: Transactions of the Moscow Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0077-1554-2013-00208-3

zbMATH Keywords

parallelohedronindex of a faceMinkowski-Venkov criterion for parallelohedrastandard faceVoronoĭ's conjecture on parallelohedra

Mathematics Subject Classification ID

(n)-dimensional polytopes (52B11) Special polytopes (linear programming, centrally symmetric, etc.) (52B12) Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20)

Related Items (5)

On Voronoi’s conjecture for four- and five-dimensional parallelohedra ⋮ An integer parallelotope with small surface area ⋮ Polytopal balls arising in optimization ⋮ A class of affinely equivalent Voronoi parallelohedra ⋮ Fullerenes and disk-fullerenes

Cites Work

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• Boris Nikolaevich Delone (Delaunay): life and work
• Properties of faces of parallelohedra
• Zonotopes, dicings, and Voronoi's conjecture on parallelohedra
• An extension of Voronoï's theorem on primitive parallelotopes
• The extension theorem
• There are exactly 222 \(L\)-types of primitive five-dimensional lattices
• The Voronoi conjecture for parallelohedra with simply connected \(\delta\)-surfaces
• An upper bound for a valence of a face in a parallelohedral tiling
• Affine Equivalent Classes of Parallelohedra
• The contraction types of parallelohedra inE⁵
• Convex bodies which tile space by translation
• Lectures on Polytopes
• Minkowski's theorems on parallelohedra and their generalisations

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