Hyperbolic space groups and their supergroups for fundamental simplex tilings

DOI10.1007/s10474-017-0761-zzbMath1399.51015OpenAlexW2764273449MaRDI QIDQ681561

Juan-Miguel Gracia

Publication date: 12 February 2018

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10474-017-0761-z

zbMATH Keywords

isometryfundamental domainPoincaré algorithmhyperbolic space grouptruncated simplex

Mathematics Subject Classification ID

Reflection and Coxeter groups (group-theoretic aspects) (20F55) Polyhedra and polytopes; regular figures, division of spaces (51M20) Other geometric groups, including crystallographic groups (20H15) Tilings in (n) dimensions (aspects of discrete geometry) (52C22)

Related Items (3)

Hyperbolic space groups with truncated simplices as fundamental domains ⋮ Congruent and non-congruent hyperball packings related to doubly truncated Coxeter orthoschemes in hyperbolic 3-space ⋮ An upper bound of the density for packing of congruent hyperballs in hyperbolic \(3\)-space

Cites Work

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• The projective interpretation of the eight 3-dimensional homogeneous geometries
• Supergroups for six series of hyperbolic simplex groups
• On Poincaré's theorem for fundamental polygons
• Fundamental simplices with outer vertices for hyperbolic groups and their group extensions for truncations
• Coxeter groups as automorphism groups of solid transitive 3-simplex tilings

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