Israel Journal of Mathematics

, Volume 43, Issue 4, pp 291–314

Neighborly polytopes

  • Ido Shemer

DOI: 10.1007/BF02761235

Cite this article as:
Shemer, I. Israel J. Math. (1982) 43: 291. doi:10.1007/BF02761235


A 2m-polytopeQ isneighborly if eachm vertices ofQ determine a face. It is shown that the combinatorial structure of a neighborly 2m-polytope determines the combinatorial structure of every subpolytope. We develop a construction of “sewing a vertex onto a polytope”, which, when applied to a neighborly 2m-polytope, yields a neighborly 2m-polytope with one more, vertex. Using this construction, we show that the numberg(2m+β,2m) of combinatorial types of neighborly 2m-polytopes with 2m+β vertices grows superexponentially as β→∞ (m≧2 fixed) and asm→∞ (β≧4 fixed).

Copyright information

© Hebrew University 1982

Authors and Affiliations

  • Ido Shemer

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