On the Voronoi Conjecture for Combinatorially Voronoi Parallelohedra in Dimension 5

DOI10.1137/18M1235004zbMath1453.52014arXiv1812.02964WikidataQ123166856 ScholiaQ123166856MaRDI QIDQ5139664

Alexander Magazinov, Mathieu Dutour Sikirić, Alexey I. Garber

Publication date: 10 December 2020

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.02964

zbMATH Keywords

tilingVoronoi conjectureparallelohedron

Mathematics Subject Classification ID

Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Polyhedral manifolds (52B70)

Related Items (1)

On Combinatorics of Voronoi Polytopes for Perturbations of the Dual Root Lattices

Uses Software

• GAP
• SageMath
• simpcomp
• Python
• Polyhedral

Cites Work

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• Computational approaches to lattice packing and covering problems
• Regular Dirichlet-Voronoi partitions for the second triclinic group
• Zonotopes, dicings, and Voronoi's conjecture on parallelohedra
• On \(\pi\)-surfaces of four-dimensional parallelohedra
• Properties of parallelotopes equivalent to Voronoi's conjecture
• Uniquely scaled dual cells
• The Voronoi conjecture for parallelohedra with simply connected \(\delta\)-surfaces
• Complexity and algorithms for computing Voronoi cells of lattices
• Convex bodies which tile space by translation
• Space tiling zonotopes
• The complete classification of five-dimensional Dirichlet–Voronoi polyhedra of translational lattices
• On the enumeration of the combinatorial types of primitive parallelohedra inE^d, 2 ≤d≤ 6

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