Geodesic
Neighbourly polytopes with few vertices
Sbornik. Mathematics, Tome 202 (2011) no. 10, pp. 1441-1462 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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R. A. Devyatov. Neighbourly polytopes with few vertices. Sbornik. Mathematics, Tome 202 (2011) no. 10, pp. 1441-1462. http://geodesic.mathdoc.fr/item/SM_2011_202_10_a1/

[1] G. M. Ziegler, Lectures on polytopes, Grad. Texts in Math., 152, Springer-Verlag, Berlin, 1995 | MR | Zbl

[2] P. McMullen, “On the upper-bound conjecture for convex polytopes”, J. Combinatorial Theory Ser. B, 10:3 (1971), 187–200 | DOI | MR | Zbl

[3] I. Shemer, “Neighborly polytopes”, Israel J. Math., 43:4 (1982), 291–314 | DOI | MR | Zbl

[4] I. Shemer, “Techniques for investigating neighborly polytopes”, Convexity and graph theory (Jerusalem, 1981), North-Holland Math. Stud., 87, North-Holland, Amsterdam, 1984, 283–292 | MR | Zbl

[5] B. Grünbaum, V. P. Sreedharan, “An enumeration of simplicial 4-polytopes with 8 vertices”, J. Combinatorial Theory, 2:4 (1967), 437–465 | DOI | MR | Zbl

[6] D. Barnette, “A family of neighborly polytopes”, Israel J. Math., 39:1–2 (1981), 127–140 | DOI | MR | Zbl

[7] J. Bokowski, I. Shemer, “Neighborly 6-polytopes with 10 vertices”, Israel J. Math., 58:1 (1987), 103–124 | DOI | MR | Zbl