Voronoi and Delaunay cells of root lattices: classification of their faces and facets by Coxeter-Dynkin diagrams

DOI10.1088/0305-4470/25/19/020zbMath0768.52010OpenAlexW1979634607MaRDI QIDQ4033633

Robert V. Moody, Jirí Patera

Publication date: 16 May 1993

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0305-4470/25/19/020

zbMATH Keywords

Coxeter-Dynkin diagramquasicrystalsVoronoi cellsDelaunay cells

Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Statistical mechanics of crystals (82D25) Polyhedra and polytopes; regular figures, division of spaces (51M20) Simple, semisimple, reductive (super)algebras (17B20) Gale and other diagrams (52B35)

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Coxeter triangulations have good quality ⋮ Lifts for Voronoi cells of lattices ⋮ The affine Weyl group symmetry of Desargues maps and of the non-commutative Hirota-Miwa system ⋮ C₇₀, C₈₀, C₉₀and carbon nanotubes by breaking of the icosahedral symmetry of C₆₀ ⋮ Lattice-based high-dimensional Gaussian filtering and the permutohedral lattice ⋮ Group-theoretical analysis of aperiodic tilings from projections of higher-dimensional latticesB_n ⋮ Coloring the Voronoi tessellation of lattices ⋮ Affine reflection groups for tiling applications: Knot theory and DNA ⋮ Discrete and continuous cosine transform generalized to Lie groups SU(2)×SU(2) and O(5)

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