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The Numbers of Edges of 5-Polytopes with a Given Number of Vertices

  • Takuya Kusunoki
  • Satoshi MuraiEmail author
Article
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Abstract

A basic combinatorial invariant of a convex polytope P is its f-vector \(f(P)=(f_0,f_1,\dots ,f_{\dim P-1})\), where \(f_i\) is the number of i-dimensional faces of P. Steinitz characterized all possible f-vectors of 3-polytopes and Grünbaum characterized the pairs given by the first two entries of the f-vectors of 4-polytopes. In this paper, we characterize the pairs given by the first two entries of the f-vectors of 5-polytopes. The same result was also proved by Pineda-Villavicencio, Ugon and Yost independently.

Keywords

Convex polytopes Face numbers 

Mathematics Subject Classification

52B05 52B11 

Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Pure and Applied Mathematics, Graduate School of Information Science and TechnologyOsaka UniversitySuitaJapan
  2. 2.Department of Mathematics, Faculty of EducationWaseda UniversityTokyoJapan

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