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 Journal paper: R. A. Devyatov, Neighborly polytopes with few vertices

Abstract
A family of neighbourly polytopes in R2d with N=2d+4 vertices is constructed. All polytopes in the family have a planar Gale diagram of a special type, namely, with exactly d+3 black points in convex position. These Gale diagrams are parametrized by 3-trees (trees with a certain additional structure). For all polytopes in the family, the number of faces of dimension m containing a given vertex A depends only on d and m.
English translation
The paper was originally published in Russian. However, English translation exists. It is not available directly from this website due to copyright restrictions. It may be available here or here if your university or you have subscription. You can also request if from me by an email to deviatov at mccme dot ru, and I will send it to you.
Final Russian version
The final russian version can be downloaded from the paper page at the journal website (no subscription required).
Version 10 (in Russian): download pdf; download zip archive with all sources
This is the version I have submited to Sbornik: Mathematics. I hope that all misprints are corrected. However, a lot of proofs are omitted, some sections are omitted too. This version is also available as arXiv:0902.1435.
Version 3 (in Russian): download pdf; download zip archive with all sources
This version contains all proofs and some misprints are corrected. However, it does not contain two sections and some calculatiions.
Version 2 (in Russian): download pdf; download zip archive with all sources
This is the most complete version. However, it still contains some misprints and terminology mistakes. The last section contains results that have already been known. Calculations in the proof of Remark 39 (Statement 38 accroding to the previous version) are already omitted.
Version 1 (in Russian): download pdf; download zip archive with all sources
The first version. It contains no rubrication, no introduction, no abstract and even no title. It may contain a lot of misprints and terminology mistakes (usage of some terms in the sense they are used is not a common practice, however, all the definitions are given). It is available here to show calculations in the proof of Statement 38 only.
Bibliographic reference:
R. A. Devyatov, Neighbourly polytopes with few vertices, Matematicheskii Sbornik 202:10 (2011), 31–54.
Article page at the journal website
English translation: Sbornik: Mathematics, 202:10 (2011), 1441–1462.
Article page at the journal websites: 1, 2

DOI of the Russian version: 10.4213/sm7532 (link)
DOI of the English version: 10.1070/SM2011v202n10ABEH004194 (link)