Smallest polyhedral tilings of 3-tori by parallelohedra

DOI10.1007/s13366-020-00530-7zbMath1467.52028OpenAlexW3085288781MaRDI QIDQ2022357

Wolfgang Kuehnel, Ulrich Brehm

Publication date: 29 April 2021

Published in: Beiträge zur Algebra und Geometrie (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13366-020-00530-7

zbMATH Keywords

tessellation3-torusparallelohedralattice tilingquotient of lattices

Mathematics Subject Classification ID

Tilings in (n) dimensions (aspects of discrete geometry) (52C22) Polyhedral manifolds (52B70)

Cites Work

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• Tiling the torus and other space forms
• The structure of cube tilings under symmetry conditions
• Cubic tessellations of the helicosms
• The rhombidodecahedral tessellation of 3-space and a particular 15-vertex triangulation of the 3-dimensional torus
• Delaunay triangulation and triangulation of tori
• More about the 52 four-dimensional parallelotopes
• The weakly neighborly polyhedral maps on the torus
• Combinatorial d-tori with a large symmetry group
• Triangulation of the 4-dimensional torus
• Lattice triangulations of \(\mathbb{E}^3 \) and of the 3-torus
• Symmetries of equivelar 4-toroids
• Equivelar maps on the torus
• An Enumeration of the Five Parallelohedra
• Convex bodies which tile space by translation
• Symmetric Tessellations on Euclidean Space-Forms
• Abstract Regular Polytopes
• Cubic tessellations of the didicosm

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