### 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 language | English |
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Journal | Annals of Combinatorics |

DOIs | |

Publication status | Published - 2019 Jan 1 |

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### Keywords

- Convex polytopes
- Face numbers

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics