Right-angled polyhedra and hyperbolic 3-manifolds

DOI10.1070/RM9762zbMath1479.52018OpenAlexW2616482100MaRDI QIDQ5360678

Andrei Vesnin

Publication date: 26 September 2017

Published in: Russian Mathematical Surveys (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/rm9762

zbMATH Keywords

hyperbolic 3-manifoldssmall coversHamiltonian graphsright-angled reflection groupscolourings of polyhedravolumes of manifolds

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) (n)-dimensional polytopes (52B11) Three-dimensional polytopes (52B10) Discrete subgroups of Lie groups (22E40)

Related Items

Volume Estimates for Right-Angled Hyperbolic Polyhedra, Ideal right-angled polyhedra in Lobachevsky space, Conference ``Dynamics in Siberia dedicated to the 90th anniversary of B. V. Chirikov, Novosibirsk, Russia, February 26 -- March 4, 2018. Abstracts, Exploring the List of Smallest Right-Angled Hyperbolic Polyhedra, Infinite series of compact hyperbolic manifolds, as possible crystal structures, Construction of fullerenes and Pogorelov polytopes with 5-, 6- and one 7-gonal face, 𝐵-rigidity of the property to be an almost Pogorelov polytope, On the 100th anniversary of the birth of Aleksei Vasil’evich Pogorelov, Cohomological rigidity of manifolds defined by 3-dimensional polytopes, New aspects of complexity theory for 3-manifolds, Theory of families of polytopes: fullerenes and Pogorelov polytopes, On correlation of hyperbolic volumes of fullerenes with their properties, Three-dimensional right-angled polytopes of finite volume in the Lobachevsky space: combinatorics and constructions, Orientable hyperbolic 4-manifolds over the 120-cell, Constructions of families of three-dimensional polytopes, characteristic patches of fullerenes, and Pogorelov polytopes, Cohomological rigidity of families of manifolds associated with ideal right-angled hyperbolic 3-polytopes

Uses Software

• SnapPy

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The number of cusps of right-angled polyhedra in hyperbolic spaces
• Some virtually special hyperbolic 3-manifold groups
• On the optimality of the ideal right-angled 24-cell
• Three-dimensional hyperelliptic manifolds
• Convex polytopes, Coxeter orbifolds and torus actions
• Organizing volumes of right-angled hyperbolic polyhedra
• Two-sided complexity bounds for Löbell manifolds
• Volume estimates for equiangular hyperbolic Coxeter polyhedra
• Hyperplane sections of polyhedra, toroidal manifolds, and discrete groups in Lobachevskij space
• Three-dimensional hyperbolic manifolds of Löbell type
• Three-dimensional hyperbolic manifolds with general fundamental polyhedron
• Arithmetic triangle groups
• Homomorphisms of edge-colored graphs and Coxeter groups
• Dihedral branched coverings of hyperbolic orbifolds
• Cyclical edge-connectivity of fullerene graphs and \((k,6)\)-cages
• On right-angled reflection groups in hyperbolic spaces.
• The orientability of small covers and coloring simple polytopes
• Die beiden Dodekaederräume
• Über offene Abbildungen auf die 3-Sphäre
• A characterization of ideal polyhedra in hyperbolic 3-space
• Three-dimensional hyperelliptic manifolds and Hamiltonian graphs
• Three-dimensional hyperbolic manifolds of small volume with three hyperelliptic involutions
• Löbell manifolds revised
• A regular partition of Lobachevskian space
• Generation of simple quadrangulations of the sphere
• Hyperbolic four-manifolds with one cusp
• Arithmetic hyperbolic reflection groups
• Hyperbolic 4‐manifolds, colourings and mutations
• Mathematical aspects of fullerenes
• TWO-SIDED ASYMPTOTIC BOUNDS FOR THE COMPLEXITY OF SOME CLOSED HYPERBOLIC THREE-MANIFOLDS
• Computing arithmetic invariants for hyperbolic reflection groups
• Hyperbolic Structures of Arithmetic Type on Some Link Complements
• Hyperbolic reflection groups
• Constant energy surfaces of Hamiltonian systems, enumeration of three-dimensional manifolds in increasing order of complexity, and computation of volumes of closed hyperbolic manifolds
• ON THE CLASSIFICATION OF ARITHMETIC GROUPS GENERATED BY REFLECTIONS IN LOBACHEVSKY SPACES
• Every Planar Map is Four Colorable
• A representation of closed, orientable 3-manifolds as 3-fold branched coverings of 𝑆³
• Every closed orientable 3-manifold is a 3-fold branched covering space of $S^3$
• ON NON-ORIENTABLE HYPERBOLIC 3-MANIFOLDS
• Lectures on Polytopes
• The volume of hyperbolic alternating link complements
• THE ABSENCE OF DISCRETE REFLECTION GROUPS WITH NONCOMPACT FUNDAMENTAL POLYHEDRON OF FINITE VOLUME IN LOBACHEVSKY SPACE OF LARGE DIMENSION
• Small covers of the dodecahedron and the $120$-cell
• Lambert cubes and the Löbell polyhedron revisited
• Some hyperbolic three-manifolds that bound geometrically
• Regular Tessellation Link Complements
• Constructing Hyperbolic Polyhedra Using Newton's Method
• ON CONVEX POLYHEDRA IN LOBAČEVSKIĬ SPACES
• ON CONVEX POLYHEDRA OF FINITE VOLUME IN LOBAČEVSKIĬ SPACE
• Algorithmic topology and classification of 3-manifolds
• On hyperelliptic involutions of hyperbolic 3-manifolds
• All flat manifolds are cusps of hyperbolic orbifolds
• Notes on right-angled Coxeter polyhedra in hyperbolic spaces.