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

Takuya Kusunoki, Satoshi Murai

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

A basic combinatorial invariant of a convex polytope P is its f-vector f(P) = (f, f 1 , ⋯ , 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.

Original languageEnglish
Pages (from-to)89-101
Number of pages13
JournalAnnals of Combinatorics
Volume23
Issue number1
DOIs
Publication statusPublished - 2019 Mar 7

Keywords

  • Convex polytopes
  • Face numbers

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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