Parallelohedra defined by quadratic forms

DOI10.1134/S008154381501006XzbMath1326.52018MaRDI QIDQ492206

Viatcheslav Grishukhin

Publication date: 20 August 2015

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

zbMATH Keywords

quadratic formVoronoi cellpolytopescalar productparallelohedronVenkov's conditions

Mathematics Subject Classification ID

Special polytopes (linear programming, centrally symmetric, etc.) (52B12) Lattices and convex bodies (number-theoretic aspects) (11H06) Tilings in (n) dimensions (aspects of discrete geometry) (52C22)

Related Items (2)

An analog of Ordin’s theorem for parallelotopes ⋮ Layer superposition of the root lattice \(A_n\)

Cites Work

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• Delaunay and Voronoi polytopes of the root lattice \(E_{7}\) and of the dual lattice \(E^\ast_{7}\)
• Properties of faces of parallelohedra
• Zonotopes, dicings, and Voronoi's conjecture on parallelohedra
• Convex bodies which tile space by translation
• Oriented Matroids
• Minkowski's theorems on parallelohedra and their generalisations
• On the theory of mainstay parallelohedra

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