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

Takuya Kusunoki, Satoshi Murai

研究成果: Article

1 引用 (Scopus)

### 抄録

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.

元の言語 English Annals of Combinatorics https://doi.org/10.1007/s00026-019-00417-y Published - 2019 1 1

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F-vector
Polytopes
Convex Polytope
Face
Invariant

### ASJC Scopus subject areas

• Discrete Mathematics and Combinatorics

### これを引用

：: Annals of Combinatorics, 01.01.2019.

研究成果: Article

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