Neighbourly polytopes with few vertices

Journal Article · Mon Oct 31 00:00:00 EDT 2011 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2011V202N10ABEH004194; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21612593

Devyatov, Rostislav A ^[1]

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1. M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

A family of neighbourly polytopes in R{sup 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.

• OSTI ID: 21612593
• Journal Information: Sbornik. Mathematics, Vol. 202, Issue 10; Other Information: DOI: 10.1070/SM2011v202n10ABEH004194; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

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