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29 March 2024
 
  » arxiv » 0804.1813

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A characterization of simplicial polytopes with g_2 = 1
Eran Nevo ; Eyal Novinsky ;
Date 11 Apr 2008
AbstractKalai proved that the simplicial polytopes with g_2=0 are the stacked polytopes. We characterize the g_2=1 case. Specifically, we prove that every simplicial d-polytope (d>3) which is prime and with g_2=1 is combinatorially equivalent either to a join of two simplices whose dimensions add up to d (each of dimension at least 2), or to a join of a polygon with a (d-2)-simplex. Thus, every simplicial d-polytope (d>3) with g_2=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>3) with g_2=1.
Source arXiv, 0804.1813
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