Abstract
A family of neighbourly polytopes in 
with 
vertices is constructed. All polytopes in the family have a planar Gale diagram of a special type, namely, with exactly 
black points in convex position. These Gale diagrams are parametrized by 
-trees (trees with a certain additional structure). For all polytopes in the family, the number of faces of dimension 
containing a given vertex 
depends only on 
and .
Bibliography: 7 titles.