Geodesic
Neighbourly polytopes with few vertices
Sbornik. Mathematics, Tome 202 (2011) no. 10, pp. 1441-1462

Voir la notice de l'article provenant de la source Math-Net.Ru

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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     author = {R. A. Devyatov},
     title = {Neighbourly polytopes with few vertices},
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     url = {http://geodesic.mathdoc.fr/item/SM_2011_202_10_a1/}
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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/