The Voronoi conjecture for parallelohedra with simply connected \(\delta\)-surfaces

DOI10.1007/s00454-014-9660-zzbMath1316.52019arXiv1212.1019OpenAlexW2115323880WikidataQ123183359 ScholiaQ123183359MaRDI QIDQ2340405

Yanyan Li

Publication date: 16 April 2015

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.1019

zbMATH Keywords

fundamental grouphomology groupVoronoi conjectureparallelohedroncanonical scaling

Mathematics Subject Classification ID

(n)-dimensional polytopes (52B11) Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20)

Related Items (10)

On \(\pi\)-surfaces of four-dimensional parallelohedra ⋮ An analog of Ordin’s theorem for parallelotopes ⋮ On Combinatorics of Voronoi Polytopes for Perturbations of the Dual Root Lattices ⋮ On the Voronoi Conjecture for Combinatorially Voronoi Parallelohedra in Dimension 5 ⋮ Geometry of lifts of tilings of Euclidean spaces ⋮ Voronoi conjecture for special free parallelotopes ⋮ Uniquely scaled dual cells ⋮ Parallelohedra: A retrospective and new results ⋮ Characterization of the three-dimensional multiple translative tiles ⋮ A class of affinely equivalent Voronoi parallelohedra

Cites Work

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• Geometry of lifts of tilings of Euclidean spaces
• Zonotopes, dicings, and Voronoi's conjecture on parallelohedra
• The theory of quality translations with applications to tilings
• On \(\pi\)-surfaces of four-dimensional parallelohedra
• Properties of parallelotopes equivalent to Voronoi's conjecture
• A class of affinely equivalent Voronoi parallelohedra
• Convex bodies which tile space by translation
• Convex bodies which tile space by translation: Acknowledgement of priority
• On Zonotopes

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