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Sbornik: Mathematics, 2011, Volume 202, Issue 10, Pages 1441–1462
DOI: https://doi.org/10.1070/SM2011v202n10ABEH004194 (Mi sm7532) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Neighbourly polytopes with few vertices

R. A. Devyatov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (408 kB) Citations (1)
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DOI: https://doi.org/10.1070/SM2011v202n10ABEH004194
Abstract: A family of neighbourly polytopes in $\mathbb R^{2d}$ 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 $m$.
Bibliography: 7 titles.
Keywords: combinatorics of polytopes, combinatorics of a set of points, neighbourly polytopes, Gale diagrams.
Received: 29.01.2009 and 12.07.2010
Russian version:
Matematicheskii Sbornik, 2011, Volume 202, Number 10, Pages 31–54
DOI: https://doi.org/10.4213/sm7532
Bibliographic databases:
Document Type: Article
UDC: 514.172.45
MSC: 52B11, 52B35
Language: English
Original paper language: Russian
Citation: R. A. Devyatov, “Neighbourly polytopes with few vertices”, Mat. Sb., 202:10 (2011), 31–54; Sb. Math., 202:10 (2011), 1441–1462
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:40
    First page:33
     
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