Reconstructing simplicial polytopes from their graphs and affine $2$-stresses

Abstract

A conjecture of Kalai from 1994 posits that for an arbitrary $2\le k\le \lfloor d/2\rfloor$, the combinatorial type of a simplicial $d$-polytope $P$ is uniquely determined by the $(k-1)$-skeleton of $P$ (given as an abstract simplicial complex) together with the space of affine $k$-stresses on $P$. We establish the first non-trivial case of this conjecture, namely, the case of $k=2$. We also prove that for a general $k$, Kalai's conjecture holds for the class of $k$-neighborly polytopes.

13 pages, to appear in Isarel Journal of Mathematics

References in corpus (1)

• Lectures on 0/1-polytopes