  In the article, a series of neigbourly polyhedra is constructed. They have
$N=2d+4$ vertices and are embedded in $\mathbb R^{2d}$. Their (affine) Gale
diagrams in $\mathbb R^2$ have $d+3$ black points that form a convex polygon.
  These Gale diagams can be enumerated using 3-trees (trees with some
additional structure).
  Given $d$ and $m$, each of the constructed polyhedra in $\mathbb R^{2d}$ has
a fixed number of faces of dimension $m$ that contain a vertex $A$. (This
number depends on $d$ and $m$ does not depend on the polyhedron and the vertex
$A$).
