Constructions of families of three-dimensional polytopes, characteristic patches of fullerenes, and Pogorelov polytopes

DOI10.1070/IM8665zbMath1378.05196OpenAlexW2596284865MaRDI QIDQ3130360

Victor M. Buchstaber, Nikolai Erokhovets

Publication date: 22 January 2018

Published in: Izvestiya: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/im8665

zbMATH Keywords

patchesfullerenenanotube\(k\)-beltsPogorelov polytopeoperations of connected sum and addition of a beltoperations of cutting off edgespartition of a disc

Mathematics Subject Classification ID

Applications of graph theory (05C90) Three-dimensional polytopes (52B10) Graph algorithms (graph-theoretic aspects) (05C85) Molecular structure (graph-theoretic methods, methods of differential topology, etc.) (92E10)

Related Items (11)

LS-category of moment-angle manifolds and higher order Massey products ⋮ Conference ``Dynamics in Siberia dedicated to the 90th anniversary of B. V. Chirikov, Novosibirsk, Russia, February 26 -- March 4, 2018. Abstracts ⋮ Construction of fullerenes and Pogorelov polytopes with 5-, 6- and one 7-gonal face ⋮ Higher order Massey products and applications ⋮ Cohomological rigidity of manifolds defined by 3-dimensional polytopes ⋮ The set of vertices with positive curvature in a planar graph with nonnegative curvature ⋮ Theory of families of polytopes: fullerenes and Pogorelov polytopes ⋮ Three-dimensional right-angled polytopes of finite volume in the Lobachevsky space: combinatorics and constructions ⋮ Massey products, toric topology and combinatorics of polytopes ⋮ Patches with short boundaries ⋮ Cohomological rigidity of families of manifolds associated with ideal right-angled hyperbolic 3-polytopes

Uses Software

• House of Graphs

Cites Work

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• Truncations of simple polytopes and applications
• Recursive generation of IPR fullerenes
• Cyclic 7-edge-cuts in fullerene graphs
• Cyclic edge-cuts in fullerene graphs
• On cyclic edge-connectivity of fullerenes
• Organizing volumes of right-angled hyperbolic polyhedra
• Numbers of faces in disordered patches
• Three-dimensional hyperbolic manifolds of Löbell type
• On lower bounds of number of perfect matchings in fullerene graphs
• Volumes of hyperbolic Löbell 3-manifolds
• Cyclical edge-connectivity of fullerene graphs and \((k,6)\)-cages
• Pentagon-hexagon-patches with short boundaries
• House of Graphs: a database of interesting graphs
• Note on the asymptotic isomer count of large fullerenes
• A regular partition of Lobachevskian space
• Some analogues of Eberhard's theorem on convex polytopes
• Fullerenes and disk-fullerenes
• Mathematical aspects of fullerenes
• On manifolds defined by 4-colourings of simple 3-polytopes
• Lectures on Polytopes
• Convex Polytopes
• Combinatorial 2-truncated Cubes and Applications
• Combinatorics of flag simplicial 3-polytopes
• Cohomological rigidity of manifolds defined by 3-dimensional polytopes
• Right-angled polyhedra and hyperbolic 3-manifolds
• The Osgood-Schoenflies theorem revisited
• Toric Topology
• ON CONVEX POLYHEDRA IN LOBAČEVSKIĬ SPACES
• ON CONVEX POLYHEDRA OF FINITE VOLUME IN LOBAČEVSKIĬ SPACE
• The Number of Hexagons and the Simplicity of Geodesics on Certain Polyhedra
• A constructive enumeration of nanotube caps

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