An analog of Ordin’s theorem for parallelotopes

DOI10.22405/2226-8383-2018-19-2-407-420zbMath1437.52007OpenAlexW4249258761MaRDI QIDQ5109662

Viatcheslav Grishukhin

Publication date: 13 May 2020

Published in: Chebyshevskii sbornik (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/cheb663

zbMATH Keywords

parallelotopeVoronoi conjectureuniquely scaled normal vectors

Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20)

Cites Work

• Geometry of lifts of tilings of Euclidean spaces
• Parallelohedra defined by quadratic forms
• Properties of faces of parallelohedra
• The theory of quality translations with applications to tilings
• On the boundary of an extremal body
• Properties of parallelotopes equivalent to Voronoi's conjecture
• The Voronoi conjecture for parallelohedra with simply connected \(\delta\)-surfaces

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