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Article

Смежностные многогранники с небольшим числом вершин

Математический сборник. 2011. Т. 202. № 10. С. 31-54.
Р. А. Девятов
Translator: Т. Панов

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.