Several examples of neigbourly polyhedra in co-dimension 4

Details Several examples of neigbourly polyhedra in co-dimension 4 Several examples of neigbourly polyhedra in co-dimension 4

2009-02-09

arxiv.org/abs/0902.1435v1

Mathematics

Combinatorics

In russian, 25 pages, 16 figures

Scientific paper

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 $A$).

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