A characterization of simplicial polytopes with g2=1

Eran Nevo*, Eyal Novinsky

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Kalai proved that the simplicial polytopes with g2=0 are the stacked polytopes. We characterize the g2=1 case.Specifically, we prove that every simplicial d-polytope (d≥4) which is prime and with g2=1 is combinatorially equivalent either to a free sum of two simplices whose dimensions add up to d (each of dimension at least 2), or to a free sum of a polygon with a (d-2)-simplex. Thus, every simplicial d-polytope (d≥4) with g2=1 is combinatorially equivalent to a polytope obtained by stacking over a polytope as above. Moreover, the above characterization holds for any homology (d-1)-sphere (d≥4) with g2=1, and our proof takes advantage of working with this larger class of complexes.

Original languageAmerican English
Pages (from-to)387-395
Number of pages9
JournalJournal of Combinatorial Theory. Series A
Issue number2
StatePublished - Feb 2011
Externally publishedYes

Bibliographical note

Funding Information:
E-mail addresses: eranevo@math.cornell.edu (E. Nevo), eyalnov@math.huji.ac.il (E. Novinsky). 1 Research partially supported by an NSF grant DMS-0757828.


  • Graph rigidity
  • Homology sphere
  • Polytope


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