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.
- Convex polytopes
- Face numbers
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics