@article {IOPORT.06081330,
    author       = {Pournin, Lionel},
    title        = {Lifting simplicial complexes to the boundary of convex polytopes.},
    year         = {2012},
    journal      = {Discrete Mathematics},
    volume       = {312},
    number       = {19},
    issn         = {0012-365X},
    pages        = {2849-2862},
    publisher    = {Elsevier Science B.V. (North-Holland), Amsterdam},
    doi          = {10.1016/j.disc.2012.06.005},
    abstract     = {Summary: A simplicial complex $C$ on a $d$-dimensional configuration of $n$ points is $k$-regular if its faces are projected from the boundary complex of a polytope with dimension at most $d+k$. Since $C$ is obviously $(n - d - 1)$-regular, the set of all integers $k$ for which $C$ is $k$-regular is non-empty. The minimum $\delta (C)$ of this set deserves attention because of its link with flip-graph connectivity. This paper introduces a characterization of $\delta (C)$ derived from the theory of Gale transforms. Using this characterization, it is proven that $\delta (C)$ is never greater than $n - d - 2$. Several new results on flip-graph connectivity follow. In particular, it is shown that connectedness does not always hold for the subgraph induced by 3-regular triangulations in the flip-graph of a point configuration.},
    identifier   = {06081330},
}