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On valences of polyhedra

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Publication:1180555
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DOI10.1016/0097-3165(91)90062-LzbMath0739.52016OpenAlexW2030134304MaRDI QIDQ1180555

Peter Gritzmann, Rainer Höhne, D. W. Barnette

Publication date: 27 June 1992

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0097-3165(91)90062-l


zbMATH Keywords

\(f\)-vectortopological manifoldpolyhedral cell-complexpolyhedral mapsvalence of vertices


Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Polyhedral manifolds (52B70)


Related Items

An Eberhard-like theorem for pentagons and heptagons ⋮ Constructing certain families of 3‐polytopal graphs



Cites Work

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  • Polyhedral 2-manifolds in \(E^ 3\) with unusually large genus
  • All triangulations of the projective plane are geometrically realizable in \(E^ 4\).
  • Kleinste Kleinsche Flaschen mit Rand
  • Upper and lower bounds of the valence-functional
  • Bänder und Möbiusbänder in konvexen Polytopen
  • Critical points and curvature for embedded polyhedra
  • Polyhedral realization in \(R^ 3\) of triangulations of the torus and 2- manifolds in cyclic 4-polytopes
  • The toroidal analogue to Eberhard's theorem
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