Notes on right-angled Coxeter polyhedra in hyperbolic spaces.

DOI10.1007/s10711-009-9454-2zbMath1205.20048OpenAlexW1986003067MaRDI QIDQ5961899

Guillaume Dufour

Publication date: 16 September 2010

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10711-009-9454-2

zbMATH Keywords

Coxeter groupshyperbolic spaceshyperbolic geometryhyperbolic orbifoldsright-angled Coxeter polyhedraright-angled reflection groups

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Topological methods in group theory (57M07) General geometric structures on low-dimensional manifolds (57M50) Symmetry properties of polytopes (52B15) Reflection groups, reflection geometries (51F15)

Related Items (10)

The number of cusps of right-angled polyhedra in hyperbolic spaces ⋮ Ideal right-angled polyhedra in Lobachevsky space ⋮ Right-angled Coxeter polytopes, hyperbolic six-manifolds, and a problem of Siegel ⋮ Right-angled polyhedra and hyperbolic 3-manifolds ⋮ Subgroup growth of right‐angled Artin and Coxeter groups ⋮ On the optimality of the ideal right-angled 24-cell ⋮ Counting cusped hyperbolic 3-manifolds that bound geometrically ⋮ Arithmetic hyperbolic reflection groups ⋮ Hyperbolic 4‐manifolds, colourings and mutations ⋮ Infinitely many arithmetic hyperbolic rational homology 3–spheres that bound geometrically

Cites Work

• Hyperplane sections of polyhedra, toroidal manifolds, and discrete groups in Lobachevskij space
• On right-angled reflection groups in hyperbolic spaces.
• ON THE CLASSIFICATION OF ARITHMETIC GROUPS GENERATED BY REFLECTIONS IN LOBACHEVSKY SPACES

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