ARTICLE DOWNLOAD

Characterizing Face and Flag Vector Pairs for Polytopes

5$
ARTICLE DOWNLOAD

Characterizing Face and Flag Vector Pairs for Polytopes

5$

Hannah Sjöberg & Günter M. Ziegler 

Abstract

Grünbaum, Barnette, and Reay in 1974 completed the characterization of the pairs (fi,fj)(fi,fj) of face numbers of 4-dimensional polytopes. Here we obtain a complete characterization of the pairs of flag numbers (f0,f03)(f0,f03) for 4-polytopes. Furthermore, we describe the pairs of face numbers (f0,fd−1)(f0,fd−1) for d-polytopes; this description is complete for even d≥6d≥6 except for finitely many exceptional pairs that are “small” in a well-defined sense, while for odd d we show that there are also “large” exceptional pairs. Our proofs rely on the insight that “small” pairs need to be defined and to be treated separately; in the 4-dimensional case, these may be characterized with the help of the characterizations of the 4-polytopes with at most eight vertices by Altshuler and Steinberg (1984).

Only units of this product remain
Year 2020
Language English
Format PDF
DOI 10.1007/s00454-018-0044-7