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

Takuya Kusunoki, Satoshi Murai

    Research output: Contribution to journalArticle

    1 Citation (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
    JournalAnnals of Combinatorics
    DOIs
    Publication statusPublished - 2019 Jan 1

    Fingerprint

    F-vector
    Polytopes
    Convex Polytope
    Face
    Invariant

    Keywords

    • Convex polytopes
    • Face numbers

    ASJC Scopus subject areas

    • Discrete Mathematics and Combinatorics

    Cite this

    The Numbers of Edges of 5-Polytopes with a Given Number of Vertices. / Kusunoki, Takuya; Murai, Satoshi.

    In: Annals of Combinatorics, 01.01.2019.

    Research output: Contribution to journalArticle

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