A basic combinatorial invariant of a convex polytope P is its f-vector f(P) = (f0, f1, ⋯, fdimP-1), where fiis 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.
|Publication status||Published - 2017 Feb 21|
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