Properties of faces of parallelohedra

DOI10.1134/S0081543809030067zbMath1185.52020MaRDI QIDQ1048448

Nikolai P. Dolbilin

Publication date: 12 January 2010

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

zbMATH Keywords

tilingparallelohedronindex of a face

Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) (n)-dimensional polytopes (52B11) Tilings in (n) dimensions (aspects of discrete geometry) (52C22)

Related Items (15)

An isoperimetric problem for three-dimensional parallelohedra ⋮ On the sum of a parallelotope and a zonotope ⋮ An integer parallelotope with small surface area ⋮ Contact vectors of point lattices ⋮ An analog of Ordin’s theorem for parallelotopes ⋮ Geometry of lifts of tilings of Euclidean spaces ⋮ Parallelohedra defined by quadratic forms ⋮ On the orthogonal projections of Dirichlet-Voronoi cells of lattices ⋮ Layer superposition of the root lattice \(A_n\) ⋮ Lifting of parallelohedra ⋮ Voronoi conjecture for special free parallelotopes ⋮ Delaunay and Voronoi polytopes of the root lattice \(E_{7}\) and of the dual lattice \(E^\ast_{7}\) ⋮ Parallelohedra: A retrospective and new results ⋮ A class of affinely equivalent Voronoi parallelohedra ⋮ Fullerenes and disk-fullerenes

Cites Work

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• On Kalai's conjectures concerning centrally symmetric polytopes
• Zonotopes, dicings, and Voronoi's conjecture on parallelohedra
• The extension theorem
• 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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